Question 1034654: I am stuck on 4 problems. If someone could explain these I would be very grateful.
1. Express ex=5.7 in terms of natural logarithms or common logarithms to a decimal approximation, of two decimal places, for the solution.
2. Evaluate in fraction form without using a calculator: Log7 √7
3. Write this equation in its equivalent logarithmic form: 3√8 = 2
4. Find the domain of this logarithmic function: f(x)=In(x-2)2
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! 1. Express ex=5.7 in terms of natural logarithms or common logarithms to a decimal approximation, of two decimal places, for the solution.
e^x=5.7
take ln of both sides to give:
ln(e^x)=ln(5.7)
x = ln(5.7)
plug into calculator to get:
x = 1.74 (answer)
.
2. Evaluate in fraction form without using a calculator: Log7 √7
Log7(√7)
write √7 in exponent form
Log7(7^(1/2))
1/2 (answer)
.
3. Write this equation in its equivalent logarithmic form: 3√8 = 2
I'm assuming the left side is the "cube root of 8"
3√8 = 2
8^(1/3) = 2
1/3 = Log8(2) (that's log base 8 on the right side)
.
4. Find the domain of this logarithmic function: f(x)=In(x-2)2
"domain" defines all possible values of that you can use for f(x)
since we cannot take the ln of zero or a negative number
Domain is:
x >= 0 (that is x must be greater than or equal to zero)
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