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

2 Answers
Sep 10, 2016

x=2/3

Explanation:

As any number to the power of zero is one, => 4^0=1
Since 4^0=1 => 4^(3x-2)=1, => 3x-2=0
Since 3x-2=0, => 3x=2, => x=2/3

Sep 10, 2016

To solve an exponential equation, take the log of each side. Or remember that anything raised to the zero power equals 1.

Explanation:

Take the log of each side.
log4^(3x-2) =log1

By log properties, the exponent becomes a coefficient
(logx^a = alogx)
(3x-2)log4= log 1

Divide both sides by log 4
3x-2 = log1/log4

log1=0 so log1/log4 = 0

3x-2=0

Subtract 2 from each side.
3x=2

Divide each side by 3
x=2/3

OR

Remember that anything raised to the zero power equals 1
(x^0=1)

So the exponent 3x-2 must equal zero.

Solve
3x-2=0
x=2/3