Question

Logarithmic help is needed. Be sure to note the differences between logarithmic and exponential forms in each equation.

Answer 1

The pattern in converting logarithmic form to exponential form and vice versa is this:

$y=b^x\leftrightarrow\log _by=x$

For the first exponential equation that is 16 = 8^4/3, our y = 16, b = 8, and x = 4/3. Let's plug this in the logarithmic pattern.

$\begin{gathered} \log _by=x \\ \log _816=\frac{4}{3} \end{gathered}$

The logarithmic form of the first equation is log₈ 16 = 4/3.

Now, let's move to the second one.

$\log _5(15,625)=6$

b = 5, y = 15, 625, and x = 6. Let's plug these in to the exponential pattern.

$\begin{gathered} y=b^x \\ 15,625=5^6 \end{gathered}$

Hence, the exponential form of the second equation is 15, 625 = 5⁶.