Solve for x, rounding to the nearest hundredth. 3^((x)/(4))=35 Answer:

Write Equation: Write down the equation that needs to be solved. We have the equation 3^(x/4) = 35.Take Logarithm: Take the natural logarithm of both sides of the equation to remove the exponent on the left side. ln(3^(x/4)) = ln(35)Simplify Left Side: Use the logarithmic property that ln(a^b) = b*ln(a) to simplify the left side of the equation. (x/4)*ln(3) = ln(35)Solve for x: Solve for x by multiplying both sides of the equation by 4 and then dividing by ln(3). x = (4*ln(35)) / ln(3)Calculate x: Calculate the value of x using a calculator. x ≈ (4*3.555348061) / 1.098612289 x ≈ 12.92139224 / 1.098612289 x ≈ 11.76470588Round x: Round the value of x to the nearest hundredth. x ≈ 11.76

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Solve for
x, rounding to the nearest hundredth.

3^((x)/(4))=35
Answer:

Solve for $x$ , rounding to the nearest hundredth. $\newline$ $3^{\frac{x}{4}}=35$ $\newline$ Answer:

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Q. Solve for

x

, rounding to the nearest hundredth.

\newline

3^{\frac{x}{4}}=35

\newline

Answer:

Write Equation: Write down the equation that needs to be solved. $\newline$ We have the equation $3^{(x/4)} = 35$ .
Take Logarithm: Take the natural logarithm of both sides of the equation to remove the exponent on the left side. $\newline$ $\ln(3^{\frac{x}{4}}) = \ln(35)$
Simplify Left Side: Use the logarithmic property that $\ln(a^b) = b\cdot\ln(a)$ to simplify the left side of the equation. $\newline$ $\left(\frac{x}{4}\right)\cdot\ln(3) = \ln(35)$
Solve for x: Solve for x by multiplying both sides of the equation by $4$ and then dividing by $\ln(3)$ . $x = \frac{4 \cdot \ln(35)}{\ln(3)}$
Calculate x: Calculate the value of x using a calculator. $\newline$ $x \approx (4 \times 3.555348061) / 1.098612289$ $\newline$ $x \approx 12.92139224 / 1.098612289$ $\newline$ $x \approx 11.76470588$
Round $x$ : Round the value of $x$ to the nearest hundredth. $x \approx 11.76$