Answer:
To solve the equation log8(x) - 4log8(x) = 2, we can simplify it using the properties of logarithms. Here's the step-by-step solution:
Step 1: Rewrite the equation using the power rule of logarithms.
log8(x) - log8(x^4) = 2
Step 2: Combine the logarithms using the quotient rule.
log8(x / x^4) = 2
Step 3: Simplify the expression inside the logarithm.
log8(1 / x^3) = 2
Step 4: Rewrite the equation in exponential form.
8^2 = 1 / x^3
Step 5: Simplify the left side of the equation.
64 = 1 / x^3
Step 6: Take the reciprocal of both sides.
1/64 = x^3
Step 7: Simplify the right side of the equation.
x^3 = 1/64
Step 8: Take the cube root of both sides to solve for x.
x = ∛(1/64)
Step 9: Simplify the cube root.
x = 1/4
Therefore, the solution to the equation log8(x) - 4log8(x) = 2 is x = 1/4.
