How do I solve 4950logx(5)−logx(100)=25404950logx⁡(5)−logx⁡(100)=2540?

Answer 1

The first thing you want to do is condense the log terms on the left side of the equation using the properties of logs.

4950log_x(5) - log_x(100) = 2540

First, move any coefficients to be exponents on the argument (the inside) of the log term.

log_x(5⁴⁹⁵⁰) - log_x(100) = 2540

Next, we can combine into a single log term by dividing the arguments.

log_x(5⁴⁹⁵⁰/100) = 2540

Now, we need to convert to exponential form so that we can solve for x.

x²⁵⁴⁰ = 5⁴⁹⁵⁰/100

In order to solve for x, we can raise both sides to the reciprocal power.

(x²⁵⁴⁰)^1/2540 = (5⁴⁹⁵⁰/100)^1/2540

x = (5⁴⁹⁵⁰/100)^1/2540

x ≈ 22.9815