Question

Simply
2log8 + log4 - log16 ÷ log 32

Answer 1

To simplify the expression, let's work step by step:

2log8 + log4 - log16 ÷ log 32

First, let's use the properties of logarithms to simplify the expression:

2log8 can be rewritten as log8^2, which is log64.
log16 ÷ log32 can be rewritten as log16/log32.

So the expression becomes:

log64 + log4 - log16/log32

Next, let's simplify the expression further:

log64 can be rewritten as log2^6, which is 6log2.
log4 can be rewritten as log2^2, which is 2log2.

So the expression becomes:

6log2 + 2log2 - log16/log32

Next, let's simplify the expression even further:

6log2 + 2log2 can be combined as 8log2.

So the expression becomes:

8log2 - log16/log32

Finally, let's simplify the expression completely:

log16 can be rewritten as log2^4, which is 4log2.
log32 can be rewritten as log2^5, which is 5log2.

So the expression becomes:

8log2 - 4log2/5log2

The log2 terms cancel out, giving us:

8 - 4/5

Simplifying the fraction:

8 - 4/5 = 40/5 - 4/5 = 36/5

Therefore, the simplified expression is 36/5.