Question

question
write the exponential equation as a logarithmic equation.
$2^{\frac{3}{2}} = \sqrt{8}$
answer attempt 1 out of 2

Explanation:

Step1: Recall the exponential - logarithmic conversion formula

The general formula for converting an exponential equation \(a^{b}=c\) (where \(a > 0,a
eq1\)) to a logarithmic equation is \(\log_{a}c = b\).

Step2: Identify \(a\), \(b\) and \(c\) from the given exponential equation

In the exponential equation \(2^{\frac{3}{2}}=\sqrt{8}\), we have:

• The base \(a = 2\)
• The exponent \(b=\frac{3}{2}\)
• The result \(c = \sqrt{8}\)

Step3: Apply the conversion formula

Using the formula \(\log_{a}c = b\) with \(a = 2\), \(b=\frac{3}{2}\) and \(c=\sqrt{8}\), we get the logarithmic equation \(\log_{2}\sqrt{8}=\frac{3}{2}\)

Answer:

\(\log_{2}\sqrt{8}=\frac{3}{2}\)