The solution to the exponential expression 4^x = (1/8)^(x + 5) is x = 15
An exponential expression is an expression whose exponent is a variable
The following is the step to determine the solution:
The equation is given as:
4^x = (1/8)^(x + 5)
Express 4 as 2^2
2^(2x) = (1/8)^(x + 5)
Express 8 as 2^3
2^(2x) = (1/2^3)^(x + 5)
So, we have:
2^(2x) = 2^[-3(x + 5)]
Cancel out the common base
2x = -3(x + 5)
Open brackets
2x = 3x - 15
Collect like terms
2x - 3x = -15
Evaluate the difference
-x = -15
Solve
x = 15
Hence, the solution to 4^x = (1/8)^(x + 5) is x = 15
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