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Solve for
x, rounding to the nearest hundredth.

3^(x)=45
Answer:

Solve for $x$ , rounding to the nearest hundredth. $\newline$ $3^{x}=45$ $\newline$ Answer:

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Solve exponential equations using logarithms

Full solution

Q. Solve for

x

, rounding to the nearest hundredth.

\newline

3^{x}=45

\newline

Answer:

Write Equation: Write down the equation that needs to be solved. $\newline$ We have the equation $3^{x} = 45$ .
Apply Logarithm: Apply the logarithm to both sides of the equation to solve for $x$ . Taking the natural logarithm ( $\ln$ ) of both sides gives us $\ln(3^{x}) = \ln(45)$ .
Use Power Property: Use the power property of logarithms to simplify the left side of the equation. $\newline$ The power property of logarithms states that $\ln(a^b) = b\cdot\ln(a)$ . Applying this to our equation gives us $x\cdot\ln(3) = \ln(45)$ .
Isolate $x$ : Isolate $x$ by dividing both sides of the equation by $\ln(3)$ . This gives us $x = \frac{\ln(45)}{\ln(3)}$ .
Calculate x: Calculate the value of x using a calculator. $\newline$ $x = \frac{\ln(45)}{\ln(3)} \approx x = \frac{3.80666248977}{1.09861228867} \approx x = 3.4657359028.$
Round to Nearest: Round the calculated value of $x$ to the nearest hundredth. $\newline$ Rounding $x = 3.4657359028$ to the nearest hundredth gives us $x \approx 3.47$ .

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