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PLEASE HELP! I'M REALLY STUCK ON THIS ONE!

Explain how to solve 2^x + 1 = 9 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.

Respuesta :

sqdancefan

Answer:

  x = 3

Step-by-step explanation:

Subtract 1

  2^x = 8

Take the log.

  x·log(2) = log(8)

Divide by the coefficient of x.

  x = log(8)/log(2) = log₂(8)

We know that 8 = 2³, so log₂(8) = 3.

  x = 3

_____

If your equation is ...

  2^(x+1) = 9

then

  x + 1 = log(9)/log(2)

  x = log(9)/log(2) -1 . . . . . . change of base formula can be used, but isn't helpful unless you have a calculator that computes log₂(9).

  x ≈ 2.170

altavistard

Answer:

Step-by-step explanation:

I will have to assume that your equation simplifies to 2^x = 8.

Note that 8 = 2^3.

Therefore, 2^x = 2^3 yields x = 3.

If you want to use the change of base formula, do this:

log 2^x = x log 2, so our 2^x = 8 becomes x log 2 = log 8.

Then:

x = log 8 / log 2, or

x = log 2^3 / log 2, or

x = 3 log 2 / log 2, or

x = 3 (same as before).

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