Solve for xx, rounding to the nearest hundredth. 91, dot, 2, to the power x , equals, 27 91⋅2 x = 27

Given Equation: We are given the equation 91.2^x = 27 and we need to solve for x. To do this, we will take the logarithm of both sides of the equation to isolate x. We can use any logarithm base, but it's common to use base 10 or the natural logarithm (ln). Let's use the natural logarithm for this calculation.Apply Natural Logarithm: Apply the natural logarithm to both sides of the equation: ln(91.2^x) = ln(27)Simplify Left Side: Use the logarithmic property that ln(a^b) = b*ln(a) to simplify the left side of the equation: x * ln(91.2) = ln(27)Divide to Solve for x: Divide both sides of the equation by ln(91.2) to solve for x: x = ln(27) / ln(91.2)Calculate x: Use a calculator to find the values of ln(27) and ln(91.2), and then divide them to find x: x ≈ ln(27) / ln(91.2) x ≈ 3.2958 / 4.5118 x ≈ 0.7303Round to Nearest Hundredth: Round the answer to the nearest hundredth as the question prompt asks: x ≈ 0.73

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Solve for $x$ , rounding to the nearest hundredth. $91.2^x = 27$

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Q. Solve for

x

, rounding to the nearest hundredth.

91.2^x = 27

Given Equation: We are given the equation $91.2^x = 27$ and we need to solve for $x$ . To do this, we will take the logarithm of both sides of the equation to isolate $x$ . We can use any logarithm base, but it's common to use base $10$ or the natural logarithm ( $\ln$ ). Let's use the natural logarithm for this calculation.
Apply Natural Logarithm: Apply the natural logarithm to both sides of the equation: $\newline$ $\ln(91.2^x) = \ln(27)$
Simplify Left Side: Use the logarithmic property that $\ln(a^b) = b\cdot\ln(a)$ to simplify the left side of the equation: $\newline$ $x \cdot \ln(91.2) = \ln(27)$
Divide to Solve for x: Divide both sides of the equation by $\ln(91.2)$ to solve for x: $\newline$ $x = \frac{\ln(27)}{\ln(91.2)}$
Calculate $x$ : Use a calculator to find the values of $\ln(27)$ and $\ln(91.2)$ , and then divide them to find $x$ :
$x \approx \frac{\ln(27)}{\ln(91.2)}$
$x \approx \frac{3.2958}{4.5118}$
$x \approx 0.7303$
Round to Nearest Hundredth: Round the answer to the nearest hundredth as the question prompt asks: $\newline$ $x \approx 0.73$