Question

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

Answer 1

`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`

Answer 2

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`