Studdy AI Logo
Math  /  Algebra

QuestionQuestion Evaluate the function f(x)=3log⁡(x+7)+2f(x)=3 \log (x+7)+2 for x=1x=1. Round the final answer to the nearest two decimal places.

Studdy Solution

STEP 1

1. We are given the function f(x)=3log⁡(x+7)+2 f(x) = 3 \log (x+7) + 2 .
2. We need to evaluate this function for x=1 x = 1 .
3. The final answer should be rounded to the nearest two decimal places.

STEP 2

1. Substitute x=1 x = 1 into the function.
2. Simplify the expression inside the logarithm.
3. Calculate the logarithm.
4. Multiply the logarithm by 3.
5. Add 2 to the result.
6. Round the final answer to two decimal places.

STEP 3

Substitute x=1 x = 1 into the function:
f(1)=3log⁡(1+7)+2 f(1) = 3 \log (1+7) + 2

STEP 4

Simplify the expression inside the logarithm:
f(1)=3log⁡(8)+2 f(1) = 3 \log (8) + 2

STEP 5

Calculate the logarithm (assuming base 10):
log⁡(8)≈0.9031 \log (8) \approx 0.9031

STEP 6

Multiply the logarithm by 3:
3×0.9031=2.7093 3 \times 0.9031 = 2.7093

STEP 7

Add 2 to the result:
2.7093+2=4.7093 2.7093 + 2 = 4.7093

STEP 8

Round the final answer to two decimal places:
4.71 4.71
The value of f(1) f(1) rounded to two decimal places is:
4.71 \boxed{4.71}

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord