SOLUTION: Evaluate the following expressions: log3 81 log5 1/25 ln e^4 log.01

Question 172949: Evaluate the following expressions:
log3 81
log5 1/25
ln e^4
log.01
Found 2 solutions by solver91311, Earlsdon:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The rule you need to apply in each case is if and only if .

I'll show you the first one:

if and only if . So what does x have to be so that ? Since , .

Work the rest of them the same way. Note that ( is the base of the natural logarithms) and (no base specified) is the same as

You might also want to make use of the rule and remember that for all real .
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Evaluate: Remember, "the logarithm of a number is the power to which the base must be raised to equal the number".
Rewrite in exponential form:
Substitute:
The bases (3) are equal, so the exponents are equal.

-------------------------
Rewrite in exponential form:
Substitute:=
The bases are equal, so the exponents are equal.

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Apply the "power rule" for logarithms:
Substitute
or
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Rewrite in exponential form:
Substitute =
The bases are equal, so the exponents are equal.

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