Write the expression below as a single logarithm in simplest form.

Question

4log 3−log 9
b b

Answer 1

The expression can be written as a single logarithm by using logarithmic identities.

Using the power rule, 4log3 can be rewritten as log3^4:
log3^4 - log9/b

Using the quotient rule, log3^4 - log9/b can be written as a single logarithm:
log((3^4)/(9/b))

Simplifying the expression inside the logarithm:
log((81)/(9/b))

Using the reciprocal rule, 9/b can be rewritten as b/9:
log((81)/(b/9))

Multiplying the numerator by the reciprocal of the denominator, we get:
log((81)*(9/b))

Multiply the numerators and the denominators:
log(729/b)

Therefore, the expression 4log3 - log(9/b) can be simplified to log(729/b).