Where appropriate, include the approximation to the nearest ten-thousandth.
27.) log x = -3
I have the answer as -3
28.) 7 ^(4-9x)= 49 I have the answer as 2
29.) 8^x =5.2 not sure
30.) 1n x=5/8 not sure
Are these answers right?
27. Nope.
what is the log of 1/1000?
28. log base 7 each side..
4-9x=2
solve for x.
On the last two, I see no easy way to approximate. I will think on them.
27.) x=1
28.) I have x= 2/9
Not sure about the last two
29.) 8^x =5.2 not sure
30.) 1n x=5/8 not sure
Let's go through each question and explain how to arrive at the correct answer while also approximating the answer to the nearest ten-thousandth:
27.) log x = -3
To solve for x, we need to raise 10 to the power of both sides of the equation since the base of a logarithm is 10 by default. We get 10^log x = 10^-3 which simplifies to x = 0.001. The approximation to the nearest ten-thousandth is x = 0.0001.
28.) 7^(4-9x) = 49
First, we want to simplify the left side of the equation. We know that 49 is equal to 7^2. So, we can rewrite the equation as 7^(4-9x) = 7^2. Since the bases are the same, we can equate the exponents: 4 - 9x = 2. Solving for x, we get x = 2/9. The approximation to the nearest ten-thousandth is x = 0.2222.
29.) 8^x = 5.2
By taking the logarithm of both sides, we can solve for x. Log(8^x) = log(5.2). Using the logarithm properties, we can bring down the exponent: x * log(8) = log(5.2). Dividing both sides by log(8), we get x = log(5.2) / log(8). Evaluating this expression gives x ≈ 0.69897. The approximation to the nearest ten-thousandth is x ≈ 0.6990.
30.) ln x = 5/8
To solve for x, we need to take the exponential of both sides using the base e, which is Euler's number. We get e^(ln x) = e^(5/8). Since the exponential and natural logarithm are inverse functions, they cancel each other out, leaving us with x = e^(5/8). Evaluating this expression gives x ≈ 1.74693. The approximation to the nearest ten-thousandth is x ≈ 1.7469.
So, to answer your question:
27.) The correct answer is x = 0.0001.
28.) The correct answer is x ≈ 0.2222.
29.) The correct answer is x ≈ 0.6990.
30.) The correct answer is x ≈ 1.7469.