What is the approximate value of x in the equation below log_3/4 25 = 3x - 1

Solution:

Given, the logarithmic equation is \(log_{\frac{3}{4}}25=3x-1\)

We have to find the value of x.

By logarithmic property,

\(log_{b}\, a=\frac{log\, a}{log\, b}\)

Now, \(log_{\frac{3}{4}}25=\frac{log25}{log\frac{3}{4}}\)

\(\frac{log25}{log\frac{3}{4}}\) = 3x - 1

The value of log 25 = 1.3979

The value of log(3/4) = -0.1249

So, \(\frac{1.3974}{-0.1249}=3x-1\)

On simplification,

-11.189 = 3x - 1

-11.189 + 1 = 3x

-10.189 = 3x

x = -10.189/3

x = -3.396

Therefore, the approximate value of x is -3.396

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What is the approximate value of x in the equation below log_3/4 25 = 3x - 1

Summary:

The approximate value of x in the equation below log_3/4 25 = 3x - 1 is -3.396