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$2\log_{3}(x+5)=4$

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Powers with negative bases

Full solution

Q.

2\log_{3}(x+5)=4

Isolate log term: Calculate the value of the logarithmic expression by dividing both sides by $2$ to isolate the log term. $\frac{2\log_3(x+5)}{2} = \frac{4}{2}$ $\log_3(x+5) = 2$
Convert to exponential form: Convert the logarithmic equation to its exponential form. $\newline$ $3^{\log_3(x+5)} = 3^2$
Simplify exponential equation: Simplify the exponential equation. $x+5 = 3^2$ $x+5 = 9$
Solve for x: Solve for x by subtracting $5$ from both sides. $\newline$ $x = 9 - 5$ $\newline$ $x = 4$

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