Question

solve.
\log_{5}(x) = 3

Explanation:

Step1: Recall logarithm definition

The logarithmic equation \(\log_{b}(a) = c\) is equivalent to the exponential equation \(b^{c}=a\) (by the definition of logarithms, where \(b>0\), \(b
eq1\), and \(a>0\)).

Step2: Apply the definition to the given equation

For the equation \(\log_{5}(x)=3\), we have \(b = 5\), \(c = 3\), and \(a=x\). Using the equivalence from Step 1, we rewrite the logarithmic equation as an exponential equation: \(5^{3}=x\).

Step3: Calculate \(5^{3}\)

We know that \(5^{3}=5\times5\times5 = 125\). So, \(x = 125\).

Answer:

\(x = 125\)