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Chapter 3: Problem 24

Solve for \(x\). $$\log _{5} x=\frac{1}{2}$$

Short Answer

Expert verified
The solution for \(x\) is \(x = \sqrt{5}\)

Step by step solution

01

Convert Logarithmic Equation to Exponential Equation

Use the basic definition of logarithm to overwrite the given logarithmic equation \(\log_{5}x = \frac{1}{2}\) into its equivalent exponential equation - \(5^{1/2} = x\) or \(x = \sqrt{5}\). The general rule is \(log_{b}x = y\) iff \(x = b^{y}\). Here, \(b = 5\), \(x = x\), and \(y = 1/2\).
02

Solve the Exponential Equation for \(x\)

When the exponential equation \(x = \sqrt{5}\) is solved for \(x\), we find \(x = \sqrt{5}\). As \(\sqrt{5}\) is already a simplified form, no further simplification is required.

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Most popular questions from this chapter

(a) solve for \(P\) and (b) solve for \(t\). $$A=P\left(1+\frac{r}{n}\right)^{n t}$$

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