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. Since the problem is titled "Intro to Logarithms Practice 6," start by identifying the specific logarithmic expression or equation you need to work with. If the problem involves simplifying, solving, or expanding logarithms, write down the given expression clearly.
2. Recall the fundamental properties of logarithms that are often used in problems: the product rule \(\log_b(MN) = \log_b(M) + \log_b(N)\), the quotient rule \(\log_b\left(\frac{M}{N}\right) = \log_b(M) - \log_b(N)\), and the power rule \(\log_b(M^p) = p \log_b(M)\). These will help you manipulate the logarithmic expressions.
3. If the problem involves solving a logarithmic equation, try to isolate the logarithmic term on one side. Then, rewrite the logarithmic equation in its equivalent exponential form using the definition \(\log_b(A) = C \iff b^C = A\).
4. After rewriting the equation in exponential form, solve for the unknown variable by applying algebraic techniques such as factoring, expanding, or using the quadratic formula if necessary.
5. Finally, check your solutions by substituting them back into the original logarithmic equation to ensure they do not produce undefined expressions (like logarithms of zero or negative numbers), since the domain of logarithms is strictly positive real numbers.