Solve for x, rounding to the nearest hundredth. 48*3^(4x)=8 Answer:

Isolate exponential term: First, we need to isolate the exponential term on one side of the equation. To do this, we divide both sides of the equation by 48. Calculation: $ \frac{48 \cdot 3^{4x}}{48} = \frac{8}{48} $Simplify the equation: After dividing, we simplify the equation. Calculation: $ 3^{4x} = \frac{1}{6} $Take natural logarithm: Next, we take the natural logarithm (ln) of both sides to solve for the exponent. Calculation: $ \ln(3^{4x}) = \ln\left(\frac{1}{6}\right) $Rewrite using property: Using the property of logarithms that $ \ln(a^b) = b \cdot \ln(a) $, we can rewrite the left side of the equation. Calculation: $ 4x \cdot \ln(3) = \ln\left(\frac{1}{6}\right) $Solve for x: Now, we solve for x by dividing both sides by $ 4 \cdot \ln(3) $. Calculation: $ x = \frac{\ln\left(\frac{1}{6}\right)}{4 \cdot \ln(3)} $Calculate x value: We calculate the value of x using a calculator. Calculation: $ x \approx \frac{\ln\left(\frac{1}{6}\right)}{4 \cdot \ln(3)} \approx -0.56 $

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Solve for
x, rounding to the nearest hundredth.

48*3^(4x)=8
Answer:

Solve for $x$ , rounding to the nearest hundredth. $\newline$ $48 \cdot 3^{4 x}=8$ $\newline$ Answer:

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Q. Solve for

x

, rounding to the nearest hundredth.

\newline

48 \cdot 3^{4 x}=8

\newline

Answer:

Isolate exponential term: First, we need to isolate the exponential term on one side of the equation. To do this, we divide both sides of the equation by $48$ . $\newline$ Calculation: $\frac{48 \cdot 3^{4x}}{48} = \frac{8}{48}$
Simplify the equation: After dividing, we simplify the equation. $\newline$ Calculation: $3^{4x} = \frac{1}{6}$
Take natural logarithm: Next, we take the natural logarithm (ln) of both sides to solve for the exponent. $\newline$ Calculation: $\ln(3^{4x}) = \ln\left(\frac{1}{6}\right)$
Rewrite using property: Using the property of logarithms that $\ln(a^b) = b \cdot \ln(a)$ , we can rewrite the left side of the equation. $\newline$ Calculation: $4x \cdot \ln(3) = \ln\left(\frac{1}{6}\right)$
Solve for x: Now, we solve for x by dividing both sides by $4 \cdot \ln(3)$ . $\newline$ Calculation: $x = \frac{\ln\left(\frac{1}{6}\right)}{4 \cdot \ln(3)}$
Calculate x value: We calculate the value of x using a calculator. $\newline$ Calculation: $x \approx \frac{\ln\left(\frac{1}{6}\right)}{4 \cdot \ln(3)} \approx -0.56$