Solve each exponential equation. Give the exact value for x.
I work them out and they are wrong what am I doing that is not right.
8^X=1/64 -2
3^x=6 In(6) In(3)or 1.63
8^x=6.5 0.624over In2 0r 0.900
3^x=4 2In (2) 0ver In3 0r 1.26
They all look fine to me, though it took me a while to separate the problems from your answers.
If they were marked wrong, then the key is in error. As you have presented them, your answers are all correct.
thank you Steve for your help.
To solve exponential equations, you need to use logarithms. Let's go through each equation one by one:
1. 8^x = 1/64 - 2
First, simplify the right side of the equation:
1/64 - 2 = -127/64
Now, we can rewrite the equation in logarithmic form:
log base 8 (-127/64) = x
Use a calculator to evaluate the logarithm:
x ≈ -2.5
So, the exact value for x is -2.5.
2. 3^x = 6
Rewrite the equation in logarithmic form:
log base 3 (6) = x
Use a calculator to evaluate the logarithm:
x ≈ 1.63
So, the approximate value for x is 1.63.
3. 8^x = 6.5
Rewrite the equation in logarithmic form:
log base 8 (6.5) = x
Use a calculator to evaluate the logarithm:
x ≈ 0.900
So, the approximate value for x is 0.900.
4. 3^x = 4
Rewrite the equation in logarithmic form:
log base 3 (4) = x
Use a calculator to evaluate the logarithm:
x ≈ 1.26
So, the approximate value for x is 1.26.
Make sure you are using the correct base for the logarithm and double-check your calculations. Using a calculator for evaluations can help prevent errors.