Math  /  Algebra

QuestionWrite the equation in logarithmic form. 100=110^{0}=1
The equation in logarithmic form is \square ee ㅁog_

Studdy Solution

STEP 1

What is this asking? We need to rewrite an exponential equation, where 10 raised to the power of 0 equals 1, in its equivalent logarithmic form. Watch out! Remember that logarithms ask, "What power do I need to raise the base to, to get a specific number?" Don't mix up the base and the result!

STEP 2

1. Understand the Relationship
2. Rewrite in Logarithmic Form

STEP 3

Alright, let's break this down!
We've got 100=110^0 = 1.
Remember, an exponent tells us how many times to multiply the base by itself.

STEP 4

In this case, our **base** is 1010, our **exponent** is 00, and our **result** is 11.
Any number (except 0) raised to the power of 0 is **always** 1!

STEP 5

Logarithms are another way to express exponentiation.
The logarithmic form asks: "To what power must we raise the **base** to get the **result**?"

STEP 6

So, if we have 100=110^0 = 1, the logarithmic form is written as log101=0\log_{10} 1 = 0.

STEP 7

Let's dissect this: * The **base** of the logarithm, 1010, is written as a subscript.
This is the same as the base of the exponent. * The **result** of the exponent, 11, is what the logarithm is operating on. * The **exponent**, 00, is what the logarithm equals.
This is the power we need to raise the base to in order to get the result.

STEP 8

The equation 100=110^0 = 1 in logarithmic form is log101=0\log_{10} 1 = 0.

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