Final answer:
To rewrite the expression as a single logarithm, use the exponentiation property of logarithms to move the coefficient inside as an exponent, resulting in log5 (u^3v^6/w^9).
Step-by-step explanation:
To rewrite the expression 3log5 (uv^2/w^3) as a single logarithm with a coefficient of 1, we utilize one of the exponentiation properties of logarithms, which states that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number (logb(an) = n • logb(a)). This means we can move the coefficient of 3 inside the logarithm as an exponent.
We begin by expressing the coefficient as an exponent:
log5 ((uv^2/w^3)3)
Next, we apply the cubing of exponentials. For the numerator and denominator within the logarithm, we cube u and v^2 in the usual way and raise w^3 to the power of 3:
log5 (u^3v^6/w^9)
Now we have rewritten the original expression as a single logarithm with a coefficient of 1.