What is the exponential form of log_b 35=3?

1 Answer
Jun 7, 2018

b^3=35

Explanation:

Lets start with some variables

If we have a relation between a," "b," "c such that
color (blue)(a=b^c

If we apply log both sides we get

loga=logb^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 logb... so log_1 alpha isn't defined for alpha!=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