Solving Logarithmic Equations Examples

Solve 2 log x – 1 = 4.

2 log x – 1 = 4
2 log x = 5
log₁₀ x = 2.5

Notice how there wasn't a base listed in this problem. That means it is a common logarithm with base 10. The next step will be to bring each side of the equation as an exponent with a base 10.

10^{log₁₀ x} = 10^2.5
x ≈ 316.228

Solve 9^{x + 6} = 2.

Solve 2000 = 1500(1.03)^t.

Solve .