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Solve for
x, rounding to the nearest hundredth.

3^(x)=58
Answer:

Solve for $x$ , rounding to the nearest hundredth. $\newline$ $3^{x}=58$ $\newline$ Answer:

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Solve exponential equations using logarithms

Full solution

Q. Solve for

x

, rounding to the nearest hundredth.

\newline

3^{x}=58

\newline

Answer:

Apply Logarithm: Apply the logarithm to both sides of the equation $3^{x}=58$ . $\newline$ $\log(3^{x}) = \log(58)$
Use Power Property: Use the power property of logarithms to bring down the exponent. $\newline$ $x \cdot \log(3) = \log(58)$
Isolate $x$ : Isolate $x$ by dividing both sides of the equation by $\log(3)$ . $\newline$ $x = \frac{\log(58)}{\log(3)}$
Calculate $x$ : Calculate the value of $x$ using a calculator. $\newline$ $x = \frac{\log(58)}{\log(3)}$ $\newline$ $x = \frac{1.7634279935629373}{0.47712125471966244}$ $\newline$ $x = 3.6956521739130435$
Round to Nearest Hundredth: Round the value of $x$ to the nearest hundredth. $x \approx 3.70$

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