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Solve for
x, rounding to the nearest hundredth.

3^(x)=67
Answer:

Solve for $x$ , rounding to the nearest hundredth. $\newline$ $3^{x}=67$ $\newline$ Answer:

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Solve exponential equations using logarithms

Full solution

Q. Solve for

x

, rounding to the nearest hundredth.

\newline

3^{x}=67

\newline

Answer:

Apply Logarithm: Apply the logarithm to both sides of the equation $3^{x}=67$ to solve for $x$ . $\newline$ $\log(3^{x}) = \log(67)$
Use Power Property: Use the power property of logarithms to bring the exponent $x$ in front of the log. $x \cdot \log(3) = \log(67)$
Isolate x: Isolate x by dividing both sides of the equation by $\log(3)$ . $x = \frac{\log(67)}{\log(3)}$
Calculate x: Calculate the value of x using a calculator. $\newline$ $x = \frac{\log(67)}{\log(3)}$ $\newline$ $x = \frac{1.8260748027\ldots}{0.4771212547\ldots}$ $\newline$ $x = 3.826\ldots$
Round to Nearest Hundredth: Round the value of $x$ to the nearest hundredth. $x \approx 3.83$

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