Log to Exponential Form
Log to exponential form is useful to easily perform complicated numeric calculations. The logarithmic form \(log_aN = x\) can be easily transformed into exponential form as \(a^x = N\). Generally, large astronomical and scientific calculations are expressed in exponential form, and here we can use the log to exponential form of transformation.
Logarithms are sometimes transformed using antilog tables to normal form, rather than transforming into exponential form. Let us learn more about log to exponential form, and their formulas, with the help of examples, and FAQs.
1.  What Is Log to Exponential Form? 
2.  Log to Exponential Form  Formulas 
3.  Examples On Log to Exponential Form 
4.  Practice Questions 
5.  FAQs on Log to Exponential Form 
What Is Log to Exponential Form?
Log to exponential form is a common form of converting one form of a mathematical expression to another form. Both these forms help in the easy calculation of huge numeric values. Quite often in calculating huge astronomical calculations, the exponential form is presented in logarithmic form, and then the logarithmic form is converted back to exponential form. The logarithm of a number N to the base of a is equal to x, which on transforming to exponential form can be taken as a to the exponent of x is equal to N.
The above formula gives a general representation and conversion of log to exponential 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 from and antilog from requires the use of logarithmic tables for calculation.
Log to Exponential Form  Formulas
Log to exponential form requires specific formulas of logarithms and exponents. Logarithms help in easily transforming the multiplication and division across numbers into addition and subtraction. And exponentials help in working across numbers with different bases and different powers. Let us look at some of the important logs and exponent formulas.
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
Exponential Formulas
The exponential form is useful to combine and write a large expression of product of the same number with a simple formula. The exponentials are helpful to easily represent large algebraic expressions. Exponential forms are sometimes converted to logarithmic form 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
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Examples of Log to Exponential Form

Example 1: Given that \(log_5625 = 4\). Convert this log to exponential form.
Solution:
Given that \(log_5625 = 4\).
The logarithmic form \(log_aN=x\). If converted to exponential form is equal to N = a^{x}.
Hence the logarithmic form \(log_5625 = 4\), written in exponential form is equal to 625 = 5^{4}.
Therefore the exponential form of the given logarithmic expression is 625 = 5^{4}.

Example 2: Find the value of Log 72, given that log 2 = 0.301, and log 3 = 0.477.
Solution:
It is given that log 2 = 0.301, and log 3 = 0.477
We need to find the value of log 72.
Log72 = Log(8 × 9)
Log 72 = Log (2^{3} x 3^{2})
Log 72 = 3log 2 + 2log3
Log 72 = 3(0.301) + 2(0.477)
Log72 = 0.903 + 0.954
Log72 = 1.857
This could have also be computed by converting log to exponential form.
Therefore the value of log72 is 1.857.
FAQs on Log to Exponential Form
What Is Log to Exponential Form?
The log to exponential form is aiming at transforming one form of expression into another form of expression. Here the logarithmic expression \(log_aN = x\), is written in exponential form as \(a^x = N\). These forms of expression are useful to compute large astronomical and scientific values.
What Is The Formula Of Log to Exponential Form?
The formula of log to exponential form is \(log_aN = x\), is written in exponential form as \(a^x = N\). The logarithm of a number N to the base of a is equal to x, which if written in exponential form is equal to a to the exponent of x is equal to N.
How To Convert Exponential to Log Form?
The conversion of exponential form to log form is very easy. Let us understand this with the help of a simple example. The exponential form \(2^5 = 32\), if written in log form is equal to \(log_232 = 5\). The can be expressed in the form of a formula, the exponential form \(a^x = N\) if written in logarithmic form is equal to \(log_aN = x\).
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