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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 $\newline$ $0.75\times10^{\left(\frac{w}{3}\right)}=30$ $\newline$ Solve the equation for $\newline$ $w$ . Express the solution as a logarithm in base $-10$ . $\newline$ $w=$ $\newline$ $\square$ $\newline$ Approximate the value of $\newline$ $w$ . Round your answer to the nearest thousandth. $\newline$ $w\approx$

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Find the roots of factored polynomials

Full solution

Q. Consider the equation

\newline

0.75\times10^{\left(\frac{w}{3}\right)}=30

\newline

Solve the equation for

\newline

w

. Express the solution as a logarithm in base

-10

.

\newline

w=

\newline

\square

\newline

Approximate the value of

\newline

w

. Round your answer to the nearest thousandth.

\newline

w\approx

Isolate $10^{w/3}$ : Isolate $10^{w/3}$ by dividing both sides by $0.75$ : $0.75\cdot10^{w/3} = 30 \rightarrow 10^{w/3} = \frac{30}{0.75} = 40.$
Apply logarithm base $-10$ : Apply logarithm base $-10$ to both sides to solve for $w/3$ : $\log_{10}(10^{w/3}) = \log_{10}(40)$ .
Simplify using logarithm property: Simplify using the property of logarithms $\log_b(b^x) = x$ : $\frac{w}{3} = \log_{10}(40)$ .
Solve for w: Solve for w by multiplying both sides by $3$ : $w = 3 \times \log_{10}(40)$ .
Approximate $\log_{10}(40)$ : Use a calculator to approximate $\log_{10}(40)$ : $\log_{10}(40) \approx 1.602$ .
Calculate w: Calculate $w$ : $w \approx 3 \times 1.602 = 4.806$ .

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