Final answer:
The condensed expression of 5ln(2)−6ln(z−4) is ln((2^5)/(z-4)^6) using the properties of logarithms, including the power rule and the quotient rule.
Step-by-step explanation:
Condensing the expression 5ln(2)−6ln(z−4) involves using properties of logarithms. Specifically, we can apply the power rule of logarithms, which allows us to move coefficients in front of a logarithm to the exponent inside the logarithm. This rule states that a * log(b) = log(ba). Therefore, we convert the expression as follows:
- 5ln(2) becomes ln(25).
- −6ln(z−4) becomes ln((z−4)−6).
Since the logarithm of a quotient is the difference of the logarithms, we further condense the expression by applying the quotient rule: ln(a) − ln(b) = ln(a/b). The condensed expression of the original problem is thus:
ln((25)/(z−4)6)