SOLUTION: 9. Evaluate the following: a. log1/2 4 b. 1og8 64 c. log32 8 d. 1og3 81 e. pi^(log

SOLUTION: 9. Evaluate the following: a. log1/2 4 b. 1og8 64 c. log32 8 d. 1og3 81 e. pi^(log_pi 2pi)

Question 113827: 9. Evaluate the following:
a. log1/2 4
b. 1og8 64
c. log32 8
d. 1og3 81
e. pi^(log_pi 2pi)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Remember if we have , we can write it as

a)
Start with the given equation. Just set the original expression equal to y. Note: the entire is the base of the log.

Rewrite the original expression using the property I listed above

Rewrite as

Multiply the exponents

Rewrite as

Since the bases are equal, the exponents are equal. So which means

So

-------------------------------------

b)
Start with the given equation. Just set the original expression equal to y

Rewrite the original expression using the property: <===>

Rewrite as

Since the bases are equal, the exponents are equal. So

So

---------------------------------------
c)

Start with the given equation. Just set the original expression equal to y

Rewrite the original expression using the property: <===>

Rewrite as and as

Multiply the exponents

Since the bases are equal, the exponents are equal. So which means

So

---------------------------------------
d)

Start with the given equation. Just set the original expression equal to y

Rewrite the original expression using the property: <===>

Rewrite as

Since the bases are equal, the exponents are equal. So

So

---------------------------------------
e)

Start with the given expression

Break up the logarithm using the identity . Think of as 2 times .

Break up the exponent using the identity

Evaluate to get 1

Since we cannot simplify the expression any further, we cannot simplify the entire expression any further.

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