Simply

2log8 + log4 - log16 ÷ log 32

1 answer

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.
Similar Questions
  1. Simply using laws of logarithms2log8^2+2log8^3 I tried this question I failed
    1. answers icon 2 answers
    1. answers icon 3 answers
  2. Solve log4 x + log4(x-2)=log4(15)I know how do the example in my book but I don't know what I'm doing wrong here. log4 x +
    1. answers icon 2 answers
    1. answers icon 1 answer
more similar questions