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Consider the equation 14 x 10^0.5w= 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 X 1005w 100Solve The Equation For W Express The Solution As A Logarithm In Base10W Approximate The Value Of W Round Your Answer To The class=

Sagot :

Solution:

Given;

[tex]14\cdot10^{0.5w}=100[/tex]

Divide both sides by 14, we have;

[tex]\begin{gathered} \frac{14\cdot10^{0.5w}}{14}=\frac{100}{14} \\ \\ 10^{0.5w}=\frac{50}{7} \end{gathered}[/tex]

Take the logarithm of both sides; we have;

[tex]\log_{10}(10)^{0.5w}=\log_{10}(\frac{50}{7})[/tex]

Applying logarithmic laws;

[tex]0.5w=\log_{10}(\frac{50}{7})[/tex]

Divide both sides by 0.5;

[tex]\begin{gathered} \frac{0.5w}{0.5}=\frac{\log_{10}(\frac{50}{7})}{0.5} \\ \\ w=\frac{\operatorname{\log}_{10}(\frac{50}{7})}{0.5} \end{gathered}[/tex]

(b)

[tex]\begin{gathered} w=\frac{\operatorname{\log}_{10}(\frac{50}{7})}{0.5} \\ \\ w\approx1.708 \end{gathered}[/tex]

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