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Exponential to Log Form
Exponential to log form is useful to easily perform complicated calculations involving huge numeric calculations. Here the exponential form \(a^x = N\) is transformed and written in logarithmic form as \(log_aN = x\). The exponential form of a to the exponent of x is N, which is transformed such that the logarithm of N to the base of a is equal to x.
The exponential form is converted to logarithmic form and is further converted back using antilogs. Let us learn more about exponential to log form, and their formulas, with the help of examples, and FAQs.
1.  What Is Exponential to Log Form? 
2.  Exponential to Log Form  Formulas 
3.  Examples on Exponential to Log Form 
4.  Practice Questions 
5.  FAQs on Exponential to Log Form 
What Is Exponential to Log Form?
Exponential to log form is useful as it helps for easy calculation of large numeric expressions. The expressions involving multiplication and division across exponents can be transformed to addition and subtraction operations with the application of logarithms. Exponential to log form is a common means of converting one form of a mathematical expression to another form. The exponential form \(a^x = N\) is transformed and written in logarithmic form as \(Log_aN = x\). The exponential form of a to the exponent of x, which is equal to N is transformed to the logarithm of a number N to the base of a, and is equal to x.
In calculations involving huge scientific and astronomical calculations, the exponential form is transformed to logarithmic form for easy calculations. The above formula gives a general representation and conversion from exponential to log form. Generally, the exponential form is converted to logarithmic form, which is sometimes transformed using antilogs, rather than converting back to exponential form. The logarithmic form and antilog form requires the use of logarithmic tables for calculation.
Exponential to Log Form  Formulas
Exponential to log form is easy for calculations with the help of exponent formulas and logarithm formulas. The exponential form helps in representing large multiplication involving the same base, as a simple expression, and the logarithmic form helps in easily transforming the multiplication and division across numbers into addition and subtraction. Let us check some of the important exponent formulas and logarithm formulas.
Exponential Formulas
The exponential form is useful to combine and write a large expression of multiplication of the same number numerous times, into a simple formula. The exponentials are helpful to easily represent large algebraic expressions. Exponential forms are sometimes converted to logarithmic forms for easy calculation. Let us look at the below formulas of exponential form.
 a^{p} = a × a × a × a × a × a × ..... p times
 a^{p}. a^{q} = a^{p + q}
 a^{p}/a^{q} = a^{p  q}
 (a^{p})^{q} = a^{pq}
 a^{p}.b^{p} = (ab)^{p}
 a^{0} = 1
 a^{1} = a
 a^{1} = 1/a
Logarithm Formulas
Logarithmic properties are helpful to work across complex logarithmic expressions. All the general arithmetic operations across numbers are transformed into a different set of operations within logarithms. The product of two numbers, when taken within the logarithmic functions is equal to the sum of the logarithmic values of the two functions. Similarly, the operation of division is transformed into the difference of the logarithms of the two numbers. Let us look at the following important formulas of logarithms.
 logab = loga + logb
 loga/b = loga  logb
 \(log_b a = \frac{loga}{logb}\)
 loga^{x} = x loga
 \(log_1 a \) = 0
 \(log_a a \) = 1
 d/dx. Logx = 1/x
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Examples of Exponential to Log Form

Example 1: Given that \(3^7 = 2187\). Convert the given exponential to log form.
Solution:
The given exponential form is \(3^7 = 2187\).
The exponential form \(a^x = N\) if converted to logarithmic form is \(log_aN = x\).
Thus the exponential form \(3^7 = 2187\) if converted to logarithmic form is \(log_32187 = 7\).
Therefore after conversion from exponential to log form we obtain \(log_32187 = 7\).

Example 2: Convert the logarithmic form of \(log_7343 = 3\) to exponential form.
Solution:
The given logarithmic form is \(log_7343=3\).
The logarithmic form \(log_aN=x\) if converted to exponential form is \(a^x =N\).
The logarithmic form \(log_7343=3\) if converted to exponential form is \(7^3=343\).
The logarithmic to exponential form on conversion is equal to \(7^3 = 343\).
FAQs on Exponential to Log Form
What Is Exponential To Log Form in Numbers?
Exponential to log form is useful for working across large calculations. The exponential form \(a^x = N\) is converted to logarithmic form \(log_aN = x\). The exponent form of a to the exponent of x is equal to N, which on converting to logarithmic form we have log of N to the base of a is equal to x.
What Formula Is Used For Conversion From Exponential To Log Form?
The formulas of exponents and logarithms are helpful to convert exponential to log form. The exponential form of \(a^x = N\) is converted to logarithmic form \(log_aN = x\). The basic formula of exponents is a^{p} = a × a × a × a × a × a × ..... p times, and the formulas of logarithms is Logab = Loga + Logb, and Loga/b = Loga  Logb.
What Is The Process To Convert From Exponential To Log Form?
The process of converting from exponential to log form is a simple process. The exponential form \(a^x = N\) is converted to logarithmic form \(log_aN = x\) , and this simple formula is helpful to convert exponential to log form.
What Are The Advantages Of Converting From Exponential To Log Form?
The conversion from exponential form to log form helps to easily convert the multiplication and division of expressions to addition and subtraction of expression. This reduces the complexity of calculations as it can be calculated in a few quick steps.
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