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

1 Answer
Jun 7, 2018

Answer:

#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#