Solve for y. 4 log_5(y+2)=8 Write your answer in simplest form.

Isolate logarithm: Isolate the logarithm by dividing both sides by 4. \[ \log_5(y+2) = \frac{8}{4} \] \[ \log_5(y+2) = 2 \]Rewrite in exponential form: Rewrite the logarithmic equation in exponential form. \[ y + 2 = 5^2 \] \[ y + 2 = 25 \]Solve for y: Solve for y by subtracting 2 from both sides. \[ y = 25 - 2 \] \[ y = 23 \]

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Solve for $y$ . $\newline$ $4 \, \log_5 (y+2) = 8$ $\newline$ Write your answer in simplest form.

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Precalculus

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Q. Solve for

y

\newline

4 \, \log_5 (y+2) = 8

\newline

Write your answer in simplest form.

Isolate logarithm: Isolate the logarithm by dividing both sides by $4$ . $\newline$ $\log_5(y+2) = \frac{8}{4}$ $\newline$ $\log_5(y+2) = 2$
Rewrite in exponential form: Rewrite the logarithmic equation in exponential form. $\newline$ $y + 2 = 5^2$ $\newline$ $y + 2 = 25$
Solve for y: Solve for y by subtracting $2$ from both sides. $\newline$ $y = 25 - 2$ $\newline$ $y = 23$