Rewrite the expression 2logx-5log(x^2+1)+4log(x-1) as a single logarithm log A. Then the function A=___________?

Answer 1

Use the logarithm properties.

Let's use the Power Rule first. clog_ax = log_q(x^c) where c is a constant, and a is the base.

You will now have logx²-log(x²+1)⁵+log(x-1)⁴

The Product Rule and Quotient Rule will be used as commutative properties.

Product Rule formula: log_a(xy) = log_ax+log_ay. Think of products as adding something

Quotient Rule formula: log_a(x/y) = log_ax-log_ay. Think of quotients as subtracting something

Using these properties will result in the equation to be simplified to log[x²(x-1)⁴/(x²+1)⁵]