Converting log(base 4) of 16 = 2 to exponential forms

[charlesjoy]

Can you please show me how to convert the below problem to an exponential form?

log 16=2
4

 

[charlesjoy]

Re: Converting exponential forms

The number 4 falls under under and between the log and the number 16. Sorry about that.

 

[daon]

Re: Converting exponential forms

\(\displaystyle log_a(x)=b \Rightarrow x=a^b\)

So,

\(\displaystyle log_4(16)=2 \Rightarrow 16=4^2\)

 

[stapel]

Can you please show me how to convert the below problem to an exponential form?

The relationship noted in the previous reply is what you need to use (and to memorize!!):

. . . . .\(\displaystyle \mbox{For any positive base }\, b\,\mbox{ and positive value }\, y,\)
. . . . .\(\displaystyle \mbox{the following are equivalent:}\)

. . . . .\(\displaystyle y\, =\, b^{x}\, \mbox{ and }\, x\, =\, \log_b(y)\)

Plug your numbers into the pattern to get the answer. :wink: