Express as a single logarithm with a coefficient of 1. Assume that the logarithms in the given problem have the same base.
4log a-3log b+5log c
log a^4 - log b^3 + log c^5
log a^4*c^5/b^3
To express the given expression as a single logarithm with a coefficient of 1, you can use the following properties of logarithms:
1. Logarithm of a product: log(x * y) = log(x) + log(y)
2. Logarithm of a power: log(x^n) = n * log(x)
Using these properties, let's simplify the given expression step by step:
4log(a) - 3log(b) + 5log(c)
Step 1: Apply the property of logarithm of a power to each term:
log(a^4) - log(b^3) + log(c^5)
Step 2: Simplify the expression using the property of logarithm of a product:
log((a^4 * c^5) / b^3)
Therefore, the expression 4log(a) - 3log(b) + 5log(c) can be simplified to log((a^4 * c^5) / b^3) as a single logarithm with a coefficient of 1.