Solve for x. Round answers to the thousandths place.
3^x=17
5.667
2.579 <--
3.093
0.388
Given its parent function g(x)=(1/2)^x , what is the equation of the function shown.
f(x)= -2(1/2)^x+1
f(x)= -(1/2)^x-3 <-- or A
f(x)= -3(1/2)^x+1
f(x)= -(1/2)^x-1
Which expression is equal to x^4/3 times x^1/3
x^5/3 <--
x^2/3
x^5/9
x^4/9
A student is solving the equation 2^x-1=16^x+2
Step 1: 2^x-1 = 16^x+2
Step 2: 2^x-1 = (2^4)x+2
Step 3: 2^x-1 = 2^4x+8
Which is the next step?
A. x-1= 1(4x+8)
B. x-1= x+2
C. 2(x-1)=4(x+2) <--? or D
D. x-1 =-4x+8
from 2^(x-1) = 2^(4x+8)
you get
x-1 = 4x+8
Your sloppiness with parentheses makes it hard to parse the math correctly.
The other answers are correct. But I have no way to check the graph.
To solve the equation 3^x = 17 and round the answer to the thousandths place, you can take the logarithm of both sides with the base of your choice (common or natural logarithm). Let's use the natural logarithm (ln):
ln(3^x) = ln(17)
Using the logarithmic property, we can bring down the exponent:
x * ln(3) = ln(17)
Now, isolate x by dividing both sides by ln(3):
x = ln(17) / ln(3)
Using a calculator, the value of x is approximately 2.579 (rounded to the thousandths place), which matches with the second option given.
Regarding the function shown, f(x) = -(1/2)^x - 3 is the equation that matches the parent function g(x) = (1/2)^x. Comparing the options, the correct answer is the second option.
To simplify the expression x^(4/3) times x^(1/3), we can use the property of exponents that states "when multiplying powers with the same base, we add the exponents." In this case:
x^(4/3) times x^(1/3) = x^((4/3) + (1/3)) = x^(5/3)
Therefore, the expression equal to x^(4/3) times x^(1/3) is x^(5/3), as indicated.
Analyzing the steps of the equation 2^x - 1 = 16^x + 2, it seems like there is an error in step 2.
Step 2: 2^x - 1 = (2^4)x + 2
This step should actually be:
2^x - 1 = (2^4) * (x + 2)
Now, moving forward to the next step. We can simplify the right side of the equation by simplifying (2^4) * (x + 2):
2^x - 1 = 16 * (x + 2)
So, the correct next step would be:
2^x - 1 = 16x + 32
None of the options provided match this next step, as they seem to have incorrect manipulations.