Question

If Log 20 = 1.301 what is the value of Logsub100 20?

Answer 1

Answer:

$log_{100}20 = 0.6505$

Step-by-step explanation:

log20 = 1.301 (when you see only "log" with no base, it is taken as a base 10)

This basically means:

$10^{1.301} = 20$  (This is the log in exponential form)

Since we don't know what  $log_{100}20$  is equal to, we will say  $log_{100}20$ = x

So to solve for $log_{100}20$ = x, you do the same thing. (convert to exponential form)

$100^{x} =20$

Now you will notice that both of these equations are equal to 20.

Since 20 = 20,

we can say $100^{x}$ = $10^{1.301}$

Another way of saying 100, is $10^{2}$ (make the bases the same)

Now we get $10^{2x} = 10^{1.301}$      

(we get 2x because an exponent to the power of an exponent ($2^{x}$) is the same as 2 * x)

Because you have the same base, you can just ignore the 10s and focus on the exponents. So you get:

2x = 1.301

x = 0.6505