Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary.
log 8x^3=4
can someone walk me through this step by step?
log 8x^3=4
assuming base 10, that means
8x^3 = 10^4 = 10000
x^3 = 10000/8 = 10 * (10/2)^3
x = 5∛10 ≈ 10.77217
thank you so much!
could u explain to me how u got the last part though?i don't think i am putting it in my calc right because every time i do it ends up being 395.284707521047
If your question mean:
log₈( x³ ) = 4
then:
3 ∙ log₈ ( x ) = 4
log₈ ( x ) = 4 / 3
x = 8 ^ ( 4 / 3 )
x = ∛ 8⁴
x = ∛ 4096
x = 16
that's not what it means,but thanks for helping!
Sure! I can walk you through the solution step by step.
Step 1: Start with the logarithmic equation: log(8x^3) = 4.
Step 2: Use the definition of logarithms to rewrite the equation in exponential form. In general, if log(base b) (a) = c, then b^c = a. Applying this definition to our equation, we have 8x^3 = 10^4.
Step 3: Simplify the exponential equation. We know that 10^4 is equal to 10,000, so we can rewrite the equation as 8x^3 = 10,000.
Step 4: Solve for x. To isolate x, we divide both sides of the equation by 8: (8x^3)/8 = 10,000/8. Simplifying further, we have x^3 = 1,250.
Step 5: Take the cube root of both sides to solve for x. Remember that the cube root of a number is the number that, when raised to the power of 3, equals the given number. Taking the cube root of both sides, we have (x^3)^(1/3) = (1,250)^(1/3). This simplifies to x = 5.
Step 6: Check your solution. Substitute x = 5 back into the original equation log(8x^3) = 4: log(8(5)^3) = 4. Simplifying, we have log(8 * 125) = 4 and log(1000) = 4. Since log(1000) = 4, our solution is confirmed.
Therefore, the solution to the logarithmic equation log(8x^3) = 4 is x = 5, rounded to the nearest ten-thousandth.