How do you solve log(2x) - log(2^x) = log(x^2) - log(x)?

1 Answer
Jan 9, 2016

x=1

Explanation:

Typically, it is difficult to solve equations that combine polynomials, logs, and exponentials.

To make progress with this equation, you must apply log rules.

log(2x)-log(2^x)=log(x^2)-log(x)

log((2x)/(2^x))=log(x^2/x)

Because you have two equal log statements, then the pieces inside must be equal as well...

((2x)/(2^x))=(x^2/x)

simplifying...

(2x)/(2^x)=x

doing algebra...

(2x)/x=2^x

2=2^x

x=1