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log_(8)(2x+3)=2

$\log _{8}(2 x+3)=2$

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Change of base formula

Full solution

Q.

\log _{8}(2 x+3)=2

Identify base and argument: Identify the base $b$ and the argument $M$ in $\log_{8}(2x+3) = 2$ . $\newline$ $b = 8$ $\newline$ $M = 2x + 3$
Rewrite in exponential form: Rewrite the logarithmic equation in exponential form: $b^y = M$ . $8^2 = 2x + 3$
Calculate value of $8^2$ : Calculate the value of $8^2$ . $\newline$ $8^2 = 64$
Set up equation: Set up the equation $64 = 2x + 3$ .
Subtract $3$ to isolate: Subtract $3$ from both sides to isolate the term with $x$ . $\newline$ $64 - 3 = 2x$ $\newline$ $61 = 2x$
Divide both sides: Divide both sides by $2$ to solve for x. $\newline$ $\frac{61}{2} = x$ $\newline$ $x = 30.5$

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