3*5^(0.2 w)=720 What is the solution of the equation? Round your answer, if necessary, to the nearest thousandth. w~~

Isolate exponential term: First, we need to isolate the exponential term on one side of the equation. 3 * 5^(0.2 w) = 720 Divide both sides by 3 to isolate the exponential term. 5^(0.2 w) = 720 / 3 5^(0.2 w) = 240Apply logarithm: Now, apply the logarithm to both sides of the equation to solve for the exponent. log(5^(0.2 w)) = log(240) Use the power property of logarithms to bring down the exponent. 0.2 w * log(5) = log(240)Isolate w: Isolate w by dividing both sides of the equation by (0.2 * log(5)). w = log(240) / (0.2 * log(5)) Calculate the value of w using a calculator. w ≈ log(240) / (0.2 * log(5)) w ≈ 2.3802112417 / (0.2 * 0.6989700043) w ≈ 2.3802112417 / 0.13979400086 w ≈ 17.028 Round the answer to the nearest thousandth. w ≈ 17.028

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3*5^(0.2 w)=720
What is the solution of the equation?
Round your answer, if necessary, to the nearest thousandth.

w~~

$3 \cdot 5^{0.2 w}=720$ $\newline$ What is the solution of the equation? $\newline$ Round your answer, if necessary, to the nearest thousandth. $\newline$ $w \approx$

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Algebra 2

Solve exponential equations using common logarithms

Full solution

3 \cdot 5^{0.2 w}=720

\newline

What is the solution of the equation?

\newline

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

\newline

w \approx

Isolate exponential term: First, we need to isolate the exponential term on one side of the equation. $\newline$ $3 \times 5^{0.2 w} = 720$ $\newline$ Divide both sides by $3$ to isolate the exponential term. $\newline$ $5^{0.2 w} = \frac{720}{3}$ $\newline$ $5^{0.2 w} = 240$
Apply logarithm: Now, apply the logarithm to both sides of the equation to solve for the exponent. $\newline$ $\log(5^{0.2 w}) = \log(240)$ $\newline$ Use the power property of logarithms to bring down the exponent. $\newline$ $0.2 w \cdot \log(5) = \log(240)$
Isolate $w$ : Isolate $w$ by dividing both sides of the equation by $(0.2 \times \log(5))$ .
$w = \frac{\log(240)}{(0.2 \times \log(5))}$
Calculate the value of $w$ using a calculator.
$w \approx \frac{\log(240)}{(0.2 \times \log(5))}$
$w \approx \frac{2.3802112417}{(0.2 \times 0.6989700043)}$
$w \approx \frac{2.3802112417}{0.13979400086}$
$w \approx 17.028$
Round the answer to the nearest thousandth.
$w \approx 17.028$