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Solve for
x, rounding to the nearest hundredth.

3^(x)=79
Answer:

Solve for $x$ , rounding to the nearest hundredth. $\newline$ $3^{x}=79$ $\newline$ Answer:

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Solve exponential equations using logarithms

Full solution

Q. Solve for

x

, rounding to the nearest hundredth.

\newline

3^{x}=79

\newline

Answer:

Write Equation: Write down the equation that needs to be solved. $\newline$ We have the equation $3^{x} = 79$ . To solve for $x$ , we will take the logarithm of both sides.
Apply Logarithm: Apply the logarithm to both sides of the equation. $\newline$ Taking the natural logarithm (ln) of both sides gives us $\ln(3^{x}) = \ln(79)$ .
Simplify Left Side: Use the power rule of logarithms to simplify the left side of the equation. $\newline$ The power rule states that $\ln(a^b) = b \cdot \ln(a)$ . Applying this to our equation gives us $x \cdot \ln(3) = \ln(79)$ .
Isolate $x$ : Isolate $x$ by dividing both sides of the equation by $\ln(3)$ . This gives us $x = \frac{\ln(79)}{\ln(3)}$ .
Calculate x: Calculate the value of x using a calculator. $\newline$ Using a calculator, we find $x = \frac{\ln(79)}{\ln(3)} \approx 4.02535169073515$ .
Round to Nearest: Round the calculated value of $x$ to the nearest hundredth. Rounding to the nearest hundredth gives us $x \approx 4.03$ .

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