Answers:
a. 8/11
b. 4
c. 3
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Step-by-step explanation
The log rule used for part (a) is
log(M) - log(N) = log(M/N)
This log rule applies to any valid log base. The base must be the same for each of the three logs in that formula. The same can be said about the other log rules mentioned for parts (b) and (c).
So,
log(M) - log(N) = log(M/N)
log(8) - log(11) = log(8/11)
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In part (b), we use the rule that log(M) + log(N) = log(MN)
So,
log(3) + log(x) = log(12)
log(3x) = log(12)
3x = 12
x = 12/3
x = 4
Therefore, log(3) + log(4) = log(12)
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Finally in part (c) we have this log rule: log(M^N) = N*log(M)
This rule is very useful when we need to solve for the variable stuck in the exponent. It allows us to pull the exponent down.
log(27) = x*log(3)
log(3^3) = x*log(3)
3*log(3) = x*log(3)
3 = x
x = 3
This then means log(27) = 3*log(3)
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Here is a summary of the log rules used.
- log(M) - log(N) = log(M/N)
- log(M) + log(N) = log(MN)
- log(M^N) = N*log(M)
These rules apply to any valid log base. The base must be the same for all of the logs in any given row.