-4*3^(6w)=-1750 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 by dividing both sides of the equation by -4. -4*3^(6w) = -1750 3^(6w) = -1750 / -4 3^(6w) = 437.5Apply logarithm: Next, we apply the logarithm to both sides of the equation to solve for the exponent. We can use the natural logarithm (ln) for this purpose. ln(3^(6w)) = ln(437.5)Simplify using power property: Using the power property of logarithms, which states that ln(a^b) = b*ln(a), we can simplify the left side of the equation. 6w * ln(3) = ln(437.5)Isolate w: Now, we isolate w by dividing both sides of the equation by 6*ln(3). w = ln(437.5) / (6 * ln(3))Perform calculations: We perform the calculations using a calculator to find the value of w. w ≈ ln(437.5) / (6 * ln(3)) w ≈ 2.681022 / (6 * 1.098612) w ≈ 2.681022 / 6.591672 w ≈ 0.406716Round the answer: Finally, we round the answer to the nearest thousandth as requested. w ≈ 0.407

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-4*3^(6w)=-1750
What is the solution of the equation?
Round your answer, if necessary, to the nearest thousandth.

w~~

$-4 \cdot 3^{6 w}=-1750$ $\newline$ 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

-4 \cdot 3^{6 w}=-1750

\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 by dividing both sides of the equation by -4＂).$\newline\$-4\cdot3^{(6w)} = -1750$$\newline$$3^{(6w)} = \frac{-1750}{-4}$$\newline$$3^{(6w)} = 437.5$
Apply logarithm: Next, we apply the logarithm to both sides of the equation to solve for the exponent. We can use the natural logarithm (ln) for this purpose.$\newline$$\ln(3^{6w}) = \ln(437.5)$
Simplify using power property: Using the power property of logarithms, which states that $\ln(a^b) = b\cdot\ln(a)$, we can simplify the left side of the equation.$6w \cdot \ln(3) = \ln(437.5)$
Isolate w: Now, we isolate w by dividing both sides of the equation by $6\ln(3)$. $\newline$\[w = \frac{\ln(437.5)}{6 \cdot \ln(3)}\]
Perform calculations: We perform the calculations using a calculator to find the value of $w$.$w \approx \frac{\ln(437.5)}{(6 \times \ln(3))}$$w \approx \frac{2.681022}{(6 \times 1.098612)}$$w \approx \frac{2.681022}{6.591672}$$w \approx 0.406716$
Round the answer: Finally, we round the answer to the nearest thousandth as requested. $w \approx 0.407$