Question

If 6^4x = 82, what is the value of x?
Round your answer to three places.

Answer 1

`x=0.61485921`

Explanation:

The given equation is in exponential form:

`6^(4x) =82`

To find
`x` we need to write it in logarithmic form:

`b^(a) =n` ⇒
`log_(b) n=a`

`6^(4x) =82` ⇒
`log_( 6 ) 82=4x`

`2.45943684 = 4x`

`(2.45943684)/(4) = x`

`0.61485921 =x`

To prove this, we can substitute the value into the given equation

`6^(4x) =82`

`6^(4(0.61485921)) =82`

`82=82`

Therefore, the answer is
`x=0.61485921`