Question

What is the logarithmic form of the solution to 102t = 9?

Answer 1

Equivalent equations are equations that have the same value

The equation in logarithmic form is $t = \frac{\log(9)}{2}$

How to rewrite the equation

The expression is given as:

$10^{2t} = 9$

Take the logarithm of both sides

$\log(10^{2t}) = \log(9)$

Apply the power rule of logarithm

$2t\log(10) = \log(9)$

Divide both sides by log(10)

$2t = \frac{\log(9)}{\log(10)}$

Apply change of base rule

$2t = \log_{10}(9)$

Divide both sides by 2

$t = \frac{\log_{10}(9)}{2}$

Rewrite as:

$t = \frac{\log(9)}{2}$

Hence, the equation in logarithmic form is $t = \frac{\log(9)}{2}$

Read more about logarithms at:

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