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Consider the equation
0.75*10^((w)/(3))=30.
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 $0.75 \cdot 10^{\frac{w}{3}}=30$ . $\newline$ Solve the equation for $w$ . Express the solution as a logarithm in base $-10$ . $\newline$ $w=$ $\newline$ $\square$ $\newline$ Approximate the value of $w$ . Round your answer to the nearest thousandth. $\newline$ $w \approx$

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Properties of logarithms: mixed review

Full solution

Q. Consider the equation

0.75 \cdot 10^{\frac{w}{3}}=30

.

\newline

Solve the equation for

w

. Express the solution as a logarithm in base

-10

.

\newline

w=

\newline

\square

\newline

Approximate the value of

w

. Round your answer to the nearest thousandth.

\newline

w \approx

Isolate $10^{w/3}$ : Isolate $10^{w/3}$ by dividing both sides by $0.75$ . $\newline$ $0.75\cdot10^{w/3} = 30$ $\newline$ $10^{w/3} = \frac{30}{0.75}$ $\newline$ $10^{w/3} = 40$
Apply logarithm base $-10$ : Apply the logarithm base $-10$ to both sides to solve for $w/3$ . $\newline$ $\log_{10}(10^{w/3}) = \log_{10}(40)$ $\newline$ $w/3 = \log_{10}(40)$
Multiply by $3$ : Multiply both sides by $3$ to solve for $w$ . $w = 3 \times \log_{10}(40)$
Calculate $\log_{10}(40)$ : Calculate $\log_{10}(40)$ using a calculator. $\newline$ $\log_{10}(40) \approx 1.602$
Substitute value for w: Substitute the value back into the equation for w. $\newline$ $w = 3 \times 1.602$ $\newline$ $w \approx 4.806$

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