Question

Use properties of logarithms to condense the logarithmic expression. write the expression as a single logarithm whose coefficient is 1. where​ possible, evaluate logarithmic expressions. log(4x+5)-log(x)

Answer 1

We can use the quotient rule [ $\text{log}_a\frac{x}{y} = \text{log}_ax-\text{log}_ay$ ] to simplify

$\text{log}(4x + 5) - \text{log}(x)\\\text{log}(\frac{4x+5}{x})\\\text{log}(4+\frac{5}{x})$

Best of Luck!

Answer 2

$\log\left( \frac{4x + 5}{x} \right) = \log(4 + \frac{5}{x})$