Which of the following is equal to 3log7(x) + log7(y)− 1/2log7(t).

Question

Which of the following is equal to 3log₇(x) + log₇(y)− 1/2log₇(t).

In my answer i use product and quotient rule

=log₇(x^3)+log₇(y)-log₇(t^(1/2)

=log₇(x^3*y)-log₇(√t)

=log₇[(x^3*y)/√t]

But my answer was wrong in the test. Why? Could you help...

Answer 1

There are only three rules for logarithms. Given that the logarithms have the same base, one can perform the following:

1) log(a) + log(b) = log(ab)

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

3) log(a^b) = blog(a)

You have

3log₇(x) + log₇(y)− 1/2log₇(t).

log₇(x³)+log₇(y)-log₇(t^1/2)

= log₇(x³)+ log₇(y / t^1/2), using rule 2

= log₇(x³y / t^1/2) using rule 1

Your answer was correct.