How do you solve 4^(2x+3) = 1?

1 Answer
Apr 2, 2016

For this problem, we must use the rule a^n = b^m -> loga^n = logb^m

Explanation:

4^(2x + 3) = 1

log4^(2x + 3) = log1

Use the property logn^a = alogn

(2x + 3)log4 = 0

2x + 3 = 0/log4

2x + 3 = 0

2x = -3

x = -3/2

Checking we find that the solution works, since a^0 = 1 -> 4^0 = 1

Practice exercises:

Solve for x. Express your answer in terms of logx (exact values)

a) 2^(3x + 1) = 5

b) 3^(2x - 1) = 4^(3x - 7)

Challenge Problem

Solve 2^(3x) xx 5 = 3^(4x - 1)

Good luck!