Questions: Exponential and Logarithmic Functions Converting between logarithmic and exponential equat Rewrite each equation as requested. (a) Rewrite as an exponential equation. log2 32=5 (b) Rewrite as a logarithmic equation. 7^-2=1/49

Solution Steps

To solve the given problems, we need to convert between logarithmic and exponential forms.

(a) The logarithmic equation \(\log_{2} 32 = 5\) can be rewritten in exponential form. The general rule is that \(\log_{b} a = c\) is equivalent to \(b^c = a\).

(b) The exponential equation \(7^{-2} = \frac{1}{49}\) can be rewritten in logarithmic form. The general rule is that \(b^c = a\) is equivalent to \(\log_{b} a = c\).

Given the logarithmic equation: \[ \log_{2} 32 = 5 \] we can rewrite it in exponential form as: \[ 2^5 = 32 \] This confirms that the exponential form is correct.

Given the exponential equation: \[ 7^{-2} = \frac{1}{49} \] we can rewrite it in logarithmic form as: \[ \log_{7} \left(\frac{1}{49}\right) = -2 \] This shows that the logarithmic form is also correct.

Final Answer