4^x-3 = 8 (solve for x)

Question

Problem: 4^x-3 = 8

 

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Hi, could someone please explain how to solve this problem? Any help is appreciated. Thank you kindly. 

Answer 1

If this is 4^{(x - 3)} = 8, then let's re-write both sides of the equation as powers of 2.

 

4 = 2²

8 = 2³

 

(2²)^{(x - 3)} = 2³

 

2^{(2x - 6)} = 2³

 

Since the bases are now the same, namely 2, then we can equate the exponents.

 

2x - 6 = 3

2x = 9

x = 9/2