Solve for x, rounding to the nearest hundredth. 7*3^((x)/(4))=1 Answer:

Isolate exponential term: First, we need to isolate the exponential term on one side of the equation. Since we are given 7*3^((x)/(4))=1, we can divide both sides by 7 to get 3^((x)/(4)) on its own. Calculation: 3^((x)/(4)) = 1/7Solve for x: Next, we need to solve for x in the exponential equation. To do this, we can take the natural logarithm (ln) of both sides of the equation to remove the base 3 exponent. Calculation: ln(3^((x)/(4))) = ln(1/7)Simplify using logarithms: Using the property of logarithms that ln(a^b) = b*ln(a), we can simplify the left side of the equation. Calculation: (x/4)*ln(3) = ln(1/7)Multiply by 4/ln(3): Now, we solve for x by multiplying both sides of the equation by 4/ln(3). Calculation: x = (4*ln(1/7))/ln(3)Calculate numerical value of x: We can now use a calculator to find the numerical value of x. Calculation: x ≈ (4*ln(1/7))/ln(3) ≈ (4*(-1.9459101490553135))/1.0986122886681098 ≈ -7.087712930Round to nearest hundredth: Finally, we round the value of x to the nearest hundredth. Calculation: x ≈ -7.09

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Solve for
x, rounding to the nearest hundredth.

7*3^((x)/(4))=1
Answer:

Solve for $x$ , rounding to the nearest hundredth. $\newline$ $7 \cdot 3^{\frac{x}{4}}=1$ $\newline$ Answer:

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Q. Solve for

x

, rounding to the nearest hundredth.

\newline

7 \cdot 3^{\frac{x}{4}}=1

\newline

Answer:

Isolate exponential term: First, we need to isolate the exponential term on one side of the equation. Since we are given $7\cdot3^{\frac{x}{4}}=1$ , we can divide both sides by $7$ to get $3^{\frac{x}{4}}$ on its own. $\newline$ Calculation: $3^{\frac{x}{4}} = \frac{1}{7}$
Solve for $x$ : Next, we need to solve for $x$ in the exponential equation. To do this, we can take the natural logarithm ( $\ln$ ) of both sides of the equation to remove the base $3$ exponent. $\newline$ Calculation: $\ln(3^{(\frac{x}{4})}) = \ln(\frac{1}{7})$
Simplify using logarithms: Using the property of logarithms that $\ln(a^b) = b\cdot\ln(a)$ , we can simplify the left side of the equation. $\newline$ Calculation: $(\frac{x}{4})\cdot\ln(3) = \ln(\frac{1}{7})$
Multiply by $\frac{4}{\ln(3)}$ : Now, we solve for $x$ by multiplying both sides of the equation by $\frac{4}{\ln(3)}$ . $\newline$ Calculation: $x = \frac{4\cdot\ln(\frac{1}{7})}{\ln(3)}$
Calculate numerical value of x: We can now use a calculator to find the numerical value of $x$ . $\newline$ Calculation: $x \approx (4*\ln(1/7))/\ln(3) \approx (4*(-1.9459101490553135))/1.0986122886681098 \approx -7.087712930$
Round to nearest hundredth: Finally, we round the value of $x$ to the nearest hundredth. $\newline$ Calculation: $x \approx -7.09$