Math  /  Algebra

QuestionWrite 102=0.0110^{-2}=0.01 in logarithmic form.
Select one: a. log20.01=10\log _{2} 0.01=10 b. log(2)=0.01\log (-2)=0.01 c. 2log10=0.01-2 \log 10=0.01 d. log1010=2\log _{10} 10=-2 e. log(0.01)=2\log (0.01)=-2

Studdy Solution

STEP 1

What is this asking? Rewrite 102=0.0110^{-2} = 0.01 using logarithms. Watch out! Remember the relationship between exponential and logarithmic forms, and don't mix up the base and the exponent!

STEP 2

1. Understand the Relationship
2. Apply the Conversion
3. Match the Answer

STEP 3

Let's remember what a logarithm *actually* means!
The equation bx=yb^x = y is equivalent to logby=x\log_b y = x.
Here, *b* is the **base**, *x* is the **exponent**, and *y* is the **result**.

STEP 4

In simpler terms, the logarithm asks: "To what power must we raise the base (*b*) to get the result (*y*)?" The answer to that question is the exponent (*x*).

STEP 5

We're given 102=0.0110^{-2} = 0.01.
Let's **identify** our key players.
Our **base** is 1010, our **exponent** is 2-2, and our **result** is 0.010.01.

STEP 6

Now, let's **plug** these values into the logarithmic form: logby=x\log_b y = x becomes log100.01=2\log_{10} 0.01 = -2.

STEP 7

When the base is 1010, we often **shorten** log10\log_{10} to just log\log.
So, we can write our logarithmic form as log0.01=2\log 0.01 = -2.

STEP 8

Looking at the options, we see that option (e) log(0.01)=2\log (0.01) = -2 **perfectly matches** our result!

STEP 9

The correct answer is (e): log(0.01)=2\log (0.01) = -2.

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