20*7^(3y)=5 What is the solution of the equation? Round your answer, if necessary, to the nearest thousandth. y~~

Isolate exponential term: Isolate the exponential term. Divide both sides of the equation by 20 to isolate the 7^(3y) term. 20*7^(3y) = 5 7^(3y) = 5/20 7^(3y) = 1/4Divide by 20: Apply the logarithm to both sides of the equation. To solve for y, we can use the natural logarithm (ln) or the common logarithm (log). Here, we'll use the natural logarithm. ln(7^(3y)) = ln(1/4)Apply logarithm: Use the power property of logarithms. The power property of logarithms states that ln(a^b) = b*ln(a). We apply this property to simplify the left side of the equation. 3y*ln(7) = ln(1/4)Use power property: Isolate y. Divide both sides of the equation by 3*ln(7) to solve for y. y = ln(1/4) / (3*ln(7))Isolate y: Calculate the value of y using a calculator. y = ln(1/4) / (3*ln(7)) y ≈ -0.317393805 / (3*1.945910149) y ≈ -0.317393805 / 5.837730447 y ≈ -0.054355248 Round the answer to the nearest thousandth. y ≈ -0.054

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20*7^(3y)=5
What is the solution of the equation?
Round your answer, if necessary, to the nearest thousandth.

y~~

$20 \cdot 7^{3 y}=5$ $\newline$ What is the solution of the equation? $\newline$ Round your answer, if necessary, to the nearest thousandth. $\newline$ $y \approx$

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Algebra 2

Solve exponential equations using common logarithms

Full solution

20 \cdot 7^{3 y}=5

\newline

What is the solution of the equation?

\newline

Round your answer, if necessary, to the nearest thousandth.

\newline

y \approx

Isolate exponential term: Isolate the exponential term. $\newline$ Divide both sides of the equation by $20$ to isolate the $7^{3y}$ term. $\newline$ $20 \cdot 7^{3y} = 5$ $\newline$ $7^{3y} = \frac{5}{20}$ $\newline$ $7^{3y} = \frac{1}{4}$
Divide by $20$ : Apply the logarithm to both sides of the equation. $\newline$ To solve for $y$ , we can use the natural logarithm ( $\ln$ ) or the common logarithm ( $\log$ ). Here, we'll use the natural logarithm. $\newline$ $\ln(7^{3y}) = \ln(\frac{1}{4})$
Apply logarithm: Use the power property of logarithms. $\newline$ The power property of logarithms states that $\ln(a^b) = b \cdot \ln(a)$ . We apply this property to simplify the left side of the equation. $\newline$ $3y \cdot \ln(7) = \ln\left(\frac{1}{4}\right)$
Use power property: Isolate $y$ . $\newline$ Divide both sides of the equation by $3\ln(7)$ to solve for $y$ . $\newline$ $y = \frac{\ln(\frac{1}{4})}{3\ln(7)}$
Isolate y: Calculate the value of y using a calculator. $\newline$ y = $\frac{\ln(\frac{1}{4})}{3 \cdot \ln(7)}$ $\newline$ y \approx $\frac{-0.317393805}{3 \cdot 1.945910149}$ $\newline$ y \approx $\frac{-0.317393805}{5.837730447}$ $\newline$ y \approx $-0.054355248$ $\newline$ Round the answer to the nearest thousandth. $\newline$ y \approx $-0.054$