Rewrite the logarithmic equation as an exponential equation.
${\log }_{4}x=1.5$

• A. $4^x=1.5$
• B. $4^{1.5}=x$
• C. $x^4=1.5$
• D. $x^{1.5}=4$

Answer: (B)

Verified step by step guidance

1. Recall the definition of a logarithm: if \(\log_b x = y\), then the equivalent exponential form is \(b^y = x\).
2. Identify the base of the logarithm, which is 4 in this problem, and the value on the right side of the equation, which is 1.5.
3. Using the definition, rewrite \(\log_4 x = 1.5\) as an exponential equation by raising the base 4 to the power of 1.5.
4. This gives the equation \$4^{1.5} = x\(, where the base 4 is raised to the exponent 1.5, and the result equals \)x$.
5. This is the exponential form equivalent to the original logarithmic equation.