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Hello. I'm new. I am wondering if someone can help me with this problem

log5 625 =

I am new at doing logs also. I was working this with a friend and we got 3 one time and 4 the other. We could both be wrong though....... Thanks.
 
Hello, achillesg22!

\(\displaystyle \log_5(625)\)
Click to expand...
First, let \(\displaystyle \log_5(625) \:= \:x\)

Rewrite in exponential form: .\(\displaystyle 5^x \:= \:625\)

Since \(\displaystyle 625 = 5^4\), we have: .\(\displaystyle 5^x \:= \:5^4\)

We have "equal bases", so the exponents are equal: .\(\displaystyle x\, =\, 4\) *

Therefore: .\(\displaystyle \log_5(625) \:= \:4\)

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* .RULE
If we have two equal exponential expressions: .\(\displaystyle b^x \:= \:b^y\), and they have equal bases,
. . . then their exponents are equal: .\(\displaystyle x\,=\,y.\)
 
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