Math  /  Algebra

QuestionUse properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log(10x)\log (10 x) \square

Studdy Solution

STEP 1

1. We are given a logarithmic expression log(10x)\log (10x).
2. We need to expand this expression using properties of logarithms.
3. We will evaluate any logarithmic expressions that can be simplified without a calculator.

STEP 2

1. Apply the product rule for logarithms to expand the expression.
2. Evaluate any logarithmic expressions that can be simplified.

STEP 3

Apply the product rule for logarithms, which states that log(ab)=log(a)+log(b)\log(ab) = \log(a) + \log(b), to the expression log(10x)\log(10x).
log(10x)=log(10)+log(x) \log(10x) = \log(10) + \log(x)

STEP 4

Evaluate log(10)\log(10). Since the base of the logarithm is 10, log(10)=1\log(10) = 1.
log(10)=1 \log(10) = 1

STEP 5

Substitute the evaluated value back into the expression:
log(10x)=1+log(x) \log(10x) = 1 + \log(x)
This is the expanded form of the original logarithmic expression.

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