Question

question 1 of 15, step 1 of 1
write the following equation in logarithmic terms. do not simplify your answer.
17^5 = g

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 its logarithmic form is \(\log_{a}(c)=b\). This formula is based on the definition of logarithms: if \(y = \log_{a}(x)\), then \(x=a^{y}\) (and vice - versa), where \(a\) is the base of the logarithm, \(x\) is the argument of the logarithm, and \(y\) is the value of the logarithm.

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

In the given equation \(17^{5}=G\), we can see that \(a = 17\) (the base of the exponential), \(b = 5\) (the exponent), and \(c = G\) (the result of the exponential operation).

Step3: Apply the conversion formula

Using the formula \(\log_{a}(c)=b\) with \(a = 17\), \(b = 5\), and \(c = G\), we get \(\log_{17}(G)=5\).

Answer:

\(\log_{17}(G)=5\)