rewrite the expression log2^x+3log2^y-4log2^z

Question

my answer is log2 1x1^3

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1^4

Although i am marked wrong could anyone explain what im doing wrong plz

Answer 1

log2^x+3log2^y-4log2^z

log2^x+log2^3y-log2^4z

log2^(3xy/4z)

(3xy/4z)log2

Answer 2

Starting with the expression:

log(2^x) + 3log(2^y) - 4log(2^z)

Remember the rule

log(2^x) = x*log(2)

Also remember the rule that log(a) + log(b) = log(a*b)

And log(a) - log(b) = log(a/b)

Using this the expression first simplifies to:

x*log(2) + 3y*log(2) - 4z*log(2)

Combining the logs together we get.

12xyz * log(2*2/2) = 12xyz*log(2)

Answer 3

I hope this helps!