Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary.
log 8x^3=4
Can someone walk me through this?
log 8x^3 = 4
8x^3 = 10^4 = 10000
x^3 = 1250
x = 10.77217
Thank you, but can you tell me what happened to the 8? Did you divide it by 10000?
Maybe Nickie meant to type
log base 8 x^3 = 4
then
x^3 = 8^4
x^3 = (2^3)^4 = 2^12
x = 2^4 = 16
log 194
Sure, I'd love to walk you through solving this logarithmic equation with a touch of humor!
First, let's rewrite the equation in its exponential form. Remember that in logarithmic form, we have the base, the logarithm, and the result. And in the exponential form, we have the base, the exponent, and the result. So, for this equation, we can rewrite it as 8x^3 = 10^4.
Now, let's simplify it a bit further. Since 10^4 is just 10,000, we have 8x^3 = 10,000.
To solve for x, we need to isolate it on one side. Divide both sides of the equation by 8 to get x^3 = 10,000/8. We can simplify this as x^3 = 1250.
Now, taking the cube root of both sides, we have x = ∛1250.
To round to the nearest ten-thousandth - wait a second, we don't have any thousandths here! Just kidding, there's no need to round in this equation since we're dealing with whole numbers.
So, the simplified solution is x = ∛1250.
And that's it! I hope this walkthrough made you laugh and helped you solve the logarithmic equation. Good luck with your math adventures!
Sure! To solve the logarithmic equation log 8x^3 = 4, we can start by applying the definition of logarithms. The logarithmic equation can be rewritten in exponential form as:
8x^3 = 10^4
Now, we need to isolate the variable x. Divide both sides of the equation by 8:
x^3 = 10^4 / 8
Simplify the right side:
x^3 = 1250
To solve for x, we will take the cube root of both sides:
x = ∛(1250)
Now, we can use a calculator to find the cube root of 1250. Rounded to the nearest ten-thousandth, we get:
x ≈ 10.643
No. I divided 10000 by 8
That is, I divided both sides of the equation by 8.
jeez
If you are working with logarithms, you surely must remember your Algebra I !