Question

rewrite the following logarithmic equations in exponential form.
a) \\(\log_{7}(2401) = 4\\)
b) \\(\log_{36}(6) = \frac{1}{2}\\)

Explanation:

Part (a)

Step1: Recall logarithm to exponential conversion rule

The logarithmic equation \(\log_{b}(y) = x\) can be converted to exponential form as \(b^{x}=y\).

Step2: Apply the rule to \(\log_{7}(2401) = 4\)

Here, \(b = 7\), \(x = 4\), and \(y = 2401\). Substituting these values into the exponential form \(b^{x}=y\), we get \(7^{4}=2401\).

Part (b)

Step1: Recall logarithm to exponential conversion rule

The logarithmic equation \(\log_{b}(y) = x\) can be converted to exponential form as \(b^{x}=y\).

Step2: Apply the rule to \(\log_{36}(6)=\frac{1}{2}\)

Here, \(b = 36\), \(x=\frac{1}{2}\), and \(y = 6\). Substituting these values into the exponential form \(b^{x}=y\), we get \(36^{\frac{1}{2}}=6\).

Answer:

s:
a) \(7^{4}=2401\)
b) \(36^{\frac{1}{2}}=6\)