# How do you solve #log_2 x=log_5 3#?

By signing up, you agree to our Terms of Service and Privacy Policy

To solve the equation log_2(x) = log_5(3), you can use the property of logarithms that states: log_a(b) = log_c(b) / log_c(a). Applying this property to the given equation, we can rewrite it as:

log_5(3) / log_5(2) = log_5(3)

Now, since the base of the logarithms on both sides of the equation is the same (log_5), we can cancel out log_5 from both sides:

3 / log_5(2) = 3

Now, solve for log_5(2):

3 = 3 log_5(2)

Divide both sides by 3:

1 = log_5(2)

Now, rewrite log_5(2) as an exponential equation:

5^1 = 2

So, x = 2 is the solution to the equation log_2(x) = log_5(3).

By signing up, you agree to our Terms of Service and Privacy Policy

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7