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What is the logarithmic form of the solution to 102t = 9?
b* =P is equivalent to log, P=a
log, P = alog, P
log 9
t=
2
log, P-
log, P
log, b
B
2
t=
log 9
с
t=log 18
D
t=log 90

What Is The Logarithmic Form Of The Solution To 102t 9 B P Is Equivalent To Log Pa Log P Alog P Log 9 T 2 Log P Log P Log B B 2 T Log 9 С Tlog 18 D Tlog 90 class=

Sagot :

MrRoyal

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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