Solve the following logarithmic equation for x.

Question

log_4(2x-8)=log_5(4x-10)

Answer 1

To solve the equation, we first use the property of logarithms that states that if log_a(b) = log_a(c), then b = c.

So, we have:
2x - 8 = 4x - 10

Simplifying further:
2x = 4x - 2
2x - 4x = -2
-2x = -2
x = 1

Therefore, the solution to the equation log_4(2x-8) = log_5(4x-10) is x = 1.