Question

Part 2 - Find the error(s) and solve the problem correctly.

Answer 1

There are errors almost on every step.

`log_ax - log_ay =log_a(x)/(y)\\eq log_axy\\2log_axy = log_a(xy)^2 \\eq log^2_axy\\log^2_axy \\eq log_a(xy)^2\\`

To answer it, use the log properties

`log_a(xy) = log_ax + log_ay\\log_a((x)/(y)) = log_ax - log_ay\\nlog_ax = log_ax^n`

Explanation:

Step for step, one way to solve it is

`log_a2x + 2(log_ax - log_ay )\\log_a2x + 2(log_a(x)/(y) )\\log_a2x + (log_a((x)/(y))^2 )\\log_a2x + (log_a(x^2)/(y^2) )\\log_a2x(x^2)/(y^2) \\log_a(2x^3)/(y^2)`