Question

4^log base 16 of 25​

Answer 1

How do I solve 4 log (16) + 8 log (25)?

As 16=24 and 25=52, we can rewrite your expression as:

4log(24)+8log(52)

Now, log(ab)=b log(a), so we can rewrite your expression as:

4×4log(2)+8×2log(5)=16log(2)+16log(5)

Now, log(ab)=log(a)=log(b), so we can rewrite your expression as:

16log(2×5)=16log(10)

Now, the final answer depends on what base logarithms you are using.

If you are using natural logs (i.e. base e), then:

16ln(10)≈.16×2.302585≈36.841

If we are dealing with common logs (i.e. base 10 logs), then:

16lg(10)=16×1=16

If we are dealing with binary logs (i.e. base 2 logs), then:

16lb(10)≈16×3.321928≈53.151

hope it works out for you ✌️