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blsea [12.9K]
2 years ago
11

Rewrite the form In exponential form: Log100 = x

Mathematics
1 answer:
andrey2020 [161]2 years ago
6 0

Answer:

10^x=100

Step-by-step explanation:

You know how subtraction is the <em>opposite of addition </em>and division is the <em>opposite of multiplication</em>? A logarithm is the <em>opposite of an exponent</em>. You know how you can rewrite the equation 3 + 2 = 5 as 5 - 3 = 2, or the equation 3 × 2 = 6 as 6 ÷ 3 = 2? This is really useful when one of those numbers on the left is unknown. 3 + _ = 8 can be rewritten as 8 - 3 = _, 4 × _ = 12 can be rewritten as 12 ÷ 4 = _. We get all our knowns on one side and our unknown by itself on the other, and the rest is computation.

We know that 3^2=9; as a logarithm, the <em>exponent</em> gets moved to its own side of the equation, and we write the equation like this: \log_3{9}=2, which you read as "the logarithm base 3 of 9 is 2." You could also read it as "the power you need to raise 3 to to get 9 is 2."

One historical quirk: because we use the decimal system, it's assumed that an expression like \log1000 uses <em>base 10</em>, and you'd interpret it as "What power do I raise 10 to to get 1000?"

The expression \log100=x means "the power you need to raise 10 to to get 100 is x," or, rearranging: "10 to the x is equal to 100," which in symbols is 10^x=100.

(If we wanted to, we could also solve this: 10^2=100, so \log100=2)

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