Where appropriate, include the approximation to the nearest ten-thousandth.
27.) log x = -3
I have the answer as 1
28.) 7 ^(4-9x)= 49 I have the answer as 2/9
29.) 8^x =5.2 not sure
30.) 1n x=5/8 not sure
Are these answers right?
27) 10^-3 = x
x = .001
28) yes
29) take ln of both sides.
xln(8)= ln(5.2)
x = ln(5.2)/ln(8) ~ 0.7928
30) raise both sides to the e
e^ (lnx) = e^(5/8)
x=e^(5/8) ~ 1.868
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To verify whether these answers are correct, we can solve each equation step by step and check the results.
27.) log x = -3
To solve for x, we need to rewrite the equation in exponential form. In this case, we can write it as x = 10^(-3). Evaluating 10^(-3) gives us 0.001, which is indeed 1 rounded to the nearest ten-thousandth. So, your answer of 1 is correct.
28.) 7^(4-9x) = 49
In order to isolate x, we need to keep the bases the same on both sides of the equation. Since 49 can be rewritten as 7^2, let's rewrite the equation as 7^(4-9x) = 7^2.
Now, we can set the exponents equal to each other, so 4 - 9x = 2. Solving this equation step by step:
4 - 9x = 2
-9x = -2
x = -2 / -9
x = 2/9
Your answer of 2/9 is correct.
29.) 8^x = 5.2
To solve for x, we can take the logarithm of both sides of the equation. However, since the base of the exponent is 8, it would be easier to take the logarithm base 8.
logbase8(8^x) = logbase8(5.2)
By properties of logarithms, we can rewrite the equation as:
x = logbase8(5.2)
To approximate this value to the nearest ten-thousandth, you can use a calculator or math software. The approximate value is around 0.5406.
So, your answer should be approximately x = 0.5406.
30.) ln x = 5/8
To solve for x, we need to use the property of natural logarithm (ln) which states that ln(e^x) = x.
Since ln(x) = 5/8, we can rewrite it as:
x = e^(5/8)
To approximate this value to the nearest ten-thousandth, you can use a calculator or math software. The approximate value is around 2.3665.
So, your answer should be approximately x = 2.3665.
In summary:
27.) The answer is correct: x = 1.
28.) The answer is correct: x = 2/9.
29.) The answer is approximately x = 0.5406.
30.) The answer is approximately x = 2.3665.