Question

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

Answer 1

Answer:

$x=0.61485921$

Step-by-step explanation:

The given equation is in exponential form:

$6^{4x} =82$

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

$b^{a} =n$ ⇒ $log_{b} n=a$

$6^{4x} =82$ ⇒ $log_{ 6 } 82=4x$

           $2.45943684 = 4x$

              $\frac{2.45943684}{4} = x$

           $0.61485921 =x$

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 $x=0.61485921$