how to solve log basex 8=-1/2

pls help

http://www.jiskha.com/display.cgi?id=1342557692

log basex8= -1/2

so rearrange it, therefore

x^-1/2 = 8

1/root(x) = 8

8root(x)=1

root(x)=1/8

x = (1/8)^2

so ur answer for x is x= 1/64

To solve the logarithmic equation logₓ 8 = -1/2, we want to find the value of x that satisfies this equation. Here's how you can do it step by step:

Step 1: Rewrite the equation using exponential notation:
x^(-1/2) = 8

Step 2: Take the reciprocal of both sides:
1 / x^(1/2) = 8

Step 3: To eliminate the fraction, square both sides of the equation:
(1 / x^(1/2))^2 = 8^2

Simplifying further:
1 / x = 64

Step 4: Now, take the reciprocal of both sides again:
x = 1 / 64

Therefore, the solution to the equation logₓ 8 = -1/2 is x = 1/64.