Logarithmic and Exponential Equations

If a^x = a^y, then x must equal y.

If a^x = a^y, then x must be greater than y.

If a^x = a^y, then x must be less than y.

If a^x = a^y, then x and y are unrelated.

Rewrite 512 as 2^9 and set x = 9.

Rewrite 512 as 2^8 and set x = 8.

Rewrite 512 as 2^10 and set x = 10.

Rewrite 512 as 2^7 and set x = 7.

x = 0

x = 10

x = 1

x = 5

Rewrite 1/5 as 5^-1 and 125 as 5^4, then set -x = 4.

Rewrite 1/5 as 5^-2 and 125 as 5^3, then set -x = 3.

Rewrite 1/5 as 5^-1 and 125 as 5^2, then set -x = 2.

Rewrite 1/5 as 5^-1 and 125 as 5^3, then set -x = 3.

log base a of a^x equals x.

log base a of a^x equals 0.

log base a of a^x equals a.

log base a of a^x equals 1.

Take the natural log of both sides to get x = ln(14).

Take the natural log of both sides to get x = ln(12).

Take the natural log of both sides to get x = ln(15).

Take the natural log of both sides to get x = ln(13).

x = e^7

x = e^8

x = e^-8

x = e^-7

Rewrite as 10^(-2) = x, so x = 0.01.

Rewrite as 10^(-2) = x, so x = 10.

Rewrite as 10^(-2) = x, so x = 100.

Rewrite as 10^(-2) = x, so x = 1/100.

Multiply both sides by 4.

Subtract 4 from both sides.

Add 4 to both sides.

Divide both sides by 4.

Multiply both sides by 3e^x.

Divide both sides by 3e^x.

Add 3e^x to both sides and subtract 2.

Subtract 3e^x from both sides and add 2.