Solve 7^{x − 1} = 7⁴

If the bases are the same, then the exponents are the equal.	7x-1 = 74
Therefore set the exponents equal to each other and solve.	x - 1 = 4
	x = 5
Check.	75-1 = 74
	74 = 74
This method can also be used when the bases are different IF you can rewrite the equation where the bases are the same.	32-x = 9x
Since 9 is equivalent to 32, you can rewrite the equation with bases of 3.	32-x = 32x
Now that the bases are the same, you can set the exponents equal to each other and solve.	2 - x = 2x
	2 = 3x
	x = 2 3
Check.

Solve these equations on your own paper.	Click below to check your answers.
1. 3x = 36	Interactive popup. Assistance may be required. Check Your Answer 3x = 36 x = 6
2. 62x-1 = 6x+2	Interactive popup. Assistance may be required. Check Your Answer 62x-1 = 6x+2 2x - 1 = x + 2 x = 3
3. 125x = 52x-6	Interactive popup. Assistance may be required. Check Your Answer 125x = 52x-6 53x = 52x-6 3x = 2x - 6 x = -6