Consider the equation 14*10^(0.5 w)=100. Solve the equation for w. Express the solution as a logarithm in base- 10 . w=◻ Approximate the value of w. Round your answer to the nearest thousandth. w~~◻

Take Logarithm: Now, we will take the logarithm of both sides of the equation to remove the exponent on the left side. We will use the base-10 logarithm since we want to express the solution as a logarithm in base-10. log(10^(0.5 w)) = log(7.14285714...) 0.5 w * log(10) = log(7.14285714...) Since log(10) is 1, this simplifies to: 0.5 w = log(7.14285714...)Divide and Solve: Next, we divide both sides of the equation by 0.5 to solve for w. 0.5 w / 0.5 = log(7.14285714...) / 0.5 w = 2 * log(7.14285714...)Calculate Approximate Value: Now we can use a calculator to find the approximate value of w. We will round the answer to the nearest thousandth. w ≈ 2 * log(7.14285714...) w ≈ 2 * 0.853871964 w ≈ 1.707743928 Rounded to the nearest thousandth: w ≈ 1.708

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Consider the equation 14*10^(0.5 w)=100.
Solve the equation for w. Express the solution as a logarithm in base- 10 .
w=◻
Approximate the value of w. Round your answer to the nearest thousandth.
w~~◻

Consider the equation $14 \cdot 10^{0.5 w}=100$ . $\newline$ Solve the equation for $w$ . Express the solution as a logarithm in base- $10$ . $\newline$ $w = \square$ $\newline$ Approximate the value of $w$ . Round your answer to the nearest thousandth. $\newline$ $w \approx \square$

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Math Problems

Algebra 2

Convert between exponential and logarithmic form: all bases

Full solution

Q. Consider the equation

14 \cdot 10^{0.5 w}=100

\newline

Solve the equation for

w

. Express the solution as a logarithm in base-

10

\newline

w = \square

\newline

Approximate the value of

w

. Round your answer to the nearest thousandth.

\newline

w \approx \square

Take Logarithm: Now, we will take the logarithm of both sides of the equation to remove the exponent on the left side. We will use the base $-10$ logarithm since we want to express the solution as a logarithm in base $-10$ . $\newline$ $\log(10^{0.5 w}) = \log(7.14285714\ldots)$ $\newline$ $0.5 w \cdot \log(10) = \log(7.14285714\ldots)$ $\newline$ Since $\log(10)$ is $1$ , this simplifies to: $\newline$ $0.5 w = \log(7.14285714\ldots)$
Divide and Solve: Next, we divide both sides of the equation by $0.5$ to solve for $w$ . $\newline$ $0.5 w / 0.5 = \log(7.14285714...) / 0.5$ $\newline$ $w = 2 \times \log(7.14285714...)$
Calculate Approximate Value: Now we can use a calculator to find the approximate value of $w$ . We will round the answer to the nearest thousandth. $\newline$ $w \approx 2 \times \log(7.14285714...)$ $\newline$ $w \approx 2 \times 0.853871964$ $\newline$ $w \approx 1.707743928$ $\newline$ Rounded to the nearest thousandth: $\newline$ $w \approx 1.708$