# What is the exponential form of log_b 35=3?

Jun 7, 2018

${b}^{3} = 35$

#### Explanation:

If we have a relation between $a , \text{ "b," } c$ such that
color (blue)(a=b^c

If we apply log both sides we get

$\log a = \log {b}^{c}$

Which turns out to be

color (purple)(loga=clogb

Npw divding both sides by color (red)(logb

We get

color (green)(loga/logb=c* cancel(logb)/cancel(logb)

[Note: if logb=0 (b=1) it would be incorrect to divide both sides by $\log b$... so ${\log}_{1} \alpha$ isn't defined for $\alpha \ne 1$]

Which gives us color (grey)(log_b a=c

Now comparing this general equation with the one given to us...
color (indigo)(c=3
color (indigo)(a=35

And so, we again get it in form
$a = {b}^{c}$

Here
color (brown)(b^3=35