PLEASE PLEASE HELP PLEASE

Mathematics

1 answer:

kogti [31]3 years ago

3 0

Answer:

r = 6

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

PR² = PQ² + QR² , substitute values

(r + 4)² = r² + 8²

r² + 8r + 16 = r² + 64 ( subtract r² from both sides )

8r + 16 = 64 ( subtract 16 from both sides )

8r = 48 ( divide both sides by 8 )

r = 6

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Rewrite the form In exponential form: Log100 = x

andrey2020 [161]

Answer:

$10^x=100$

Step-by-step explanation:

You know how subtraction is the opposite of addition and division is the opposite of multiplication? A logarithm is the opposite of an exponent. 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 exponent 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 base 10, 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 $10^x=100$ .