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Sagot :
Equivalent equations are equations that have the same value
The equation in logarithmic form is [tex]t = \frac{\log(9)}{2}[/tex]
How to rewrite the equation
The expression is given as:
[tex]10^{2t} = 9[/tex]
Take the logarithm of both sides
[tex]\log(10^{2t}) = \log(9)[/tex]
Apply the power rule of logarithm
[tex]2t\log(10) = \log(9)[/tex]
Divide both sides by log(10)
[tex]2t = \frac{\log(9)}{\log(10)}[/tex]
Apply change of base rule
[tex]2t = \log_{10}(9)[/tex]
Divide both sides by 2
[tex]t = \frac{\log_{10}(9)}{2}[/tex]
Rewrite as:
[tex]t = \frac{\log(9)}{2}[/tex]
Hence, the equation in logarithmic form is [tex]t = \frac{\log(9)}{2}[/tex]
Read more about logarithms at:
https://brainly.com/question/25710806
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