Question

PLEASE HELP WITH THIS

Answer 1

Answer:

B

Step-by-step explanation:

The question can be written is

5^x = 75

Now take the log of both sides.

log(5x) = log(75)            Bring the x outside the brackets

x log(5) = log(75)           Divide by log 5

x = log(75)/log(5)

log 75 = 1.8751

log 5 = .8990

x = 1.8751/.8990 = 2.6826

Answer 2

Answer:

  (b)  2.68

Step-by-step explanation:

Your question has a link to a suitable calculator. All you need to do is make use of it. It tells you log₅(75) ≈ 2.68.

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Other ways to look at the problem

If you recall that a logarithm represents an exponent of the base, you can ask yourself, what power 5 must be raised to in order to get 75. You know that 5^2 = 25, and 5^3 = 125, so the power will have to be between 2 and 3. There is only one answer choice in that range: 2.68.

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The rules of logarithms let you rewrite the given expression as ...

  log₅(75) = log₅(3×5²) = log₅(3) +2·log₅(5) = log₅(3) +2

The log₅ of any number between 1 and 5 will be a positive fraction, so this sum must be between 2 and 3.