Studdy AI Logo
Math  /  Algebra

QuestionExpress as a single logarithmic expression. You do NOT need to expand exponents. Assume all expressions represent positive numbers. log⁡9(x+8)+log⁡9(x−7)=log⁡9(□)\log _{9}(x+8)+\log _{9}(x-7)=\log _{9}(\square) Question Help: Video Written Example Submit Question

Studdy Solution

STEP 1

1. We are working with logarithms with the same base, which allows us to use logarithmic properties.
2. The expressions inside the logarithms are positive, as stated in the problem.

STEP 2

1. Apply the product property of logarithms to combine the logarithmic expressions.
2. Express the combined expression as a single logarithmic expression.

STEP 3

Use the product property of logarithms, which states that log⁡b(A)+log⁡b(B)=log⁡b(A×B)\log_b(A) + \log_b(B) = \log_b(A \times B), to combine the given logarithmic expressions:
log⁡9(x+8)+log⁡9(x−7)=log⁡9((x+8)(x−7))\log_{9}(x+8) + \log_{9}(x-7) = \log_{9}((x+8)(x-7))

STEP 4

Express the combined expression as a single logarithmic expression:
The expression log⁡9((x+8)(x−7))\log_{9}((x+8)(x-7)) is already in the form of a single logarithmic expression, so we have:
log⁡9(□)=log⁡9((x+8)(x−7))\log_{9}(\square) = \log_{9}((x+8)(x-7))
Thus, the expression inside the logarithm is:
□=(x+8)(x−7)\square = (x+8)(x-7)

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