Final answer:
The solution to the exponential equation 8^0.4x = 5 is found by applying logarithm base 8 to both sides and solving for x, which entails dividing log base 8 of 5 by 0.4 and then rounding the result to four decimal places.
Step-by-step explanation:
To find the solution to the exponential equation 80.4x = 5, we need to solve for 'x'. We do this by applying logarithms. Let's use the logarithm base 8 to simplify our calculations since 8 is the base of the exponent.
First, apply the logarithm base 8 to both sides of the equation:
log8(80.4x) = log8(5)
This simplifies to:
0.4x = log8(5)
To solve for 'x', divide both sides by 0.4:
x = log8(5) / 0.4
You would then use a calculator to find log8(5) and divide it by 0.4 to get the value of x, rounded to four decimal places.