Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary.
log8x^3 = 4
Can somebody please give me a step-by-step for this? I'm usually good at this but I'm stuck for this one:(
Thanks in adv.
3*log8 (x)=4
log8 (x)=4/3
8^(4/3)=x
2^4=x
x= 16
To solve the logarithmic equation log8x^3 = 4, you need to isolate x.
Step 1: Rewrite the equation in exponential form.
In logarithmic form, log8x^3 = 4 means that 8 raised to the power of 4 is equal to x^3. So, we have 8^4 = x^3.
Step 2: Simplify.
Taking the fourth power of 8, we have 8^4 = (2^3)^4 = 2^12.
So, the equation becomes 2^12 = x^3.
Step 3: Take the cube root of both sides.
Taking the cube root of both sides of the equation, we have (∛(2^12)) = (∛x^3).
This simplifies to 2^4 = x.
Step 4: Calculate the answer.
Evaluate 2^4, which is equal to 16. Therefore, x = 16.
Therefore, the solution to the logarithmic equation log8x^3 = 4 is x = 16.