Question

Find the solution to the equation log16 32 = x + 5. Using complete sentences, explain the procedure used to solve this equation.

Answer 1

i dont get it

Answer 2

Isolate x.

Answer 3

-5log16 27

Answer 4

\(\Large
\log_{16}(32) = x + 5 \\ \Large
\log_{16}(2*16) = x + 5 \\ \Large
\log_{16}(2) + \log_{16}(16) = x + 5 \\ \Large
\log_{16}(2) + 1 = x + 5 \\ \Large
\text{Subtract 5:} \\ \Large
\log_{16}(2) -4 = x \\ \Large
x = \log_{16}(2) -4 \\ \Large
x = \frac{1}{\log_{2}(16)} -4 \\ \Large
x = \frac 14 -4 \\ \Large
x = \frac{-15}{4} \\ \Large
x = -3\frac 34
\)

Answer 5

damm

Answer 6

A quicker way to do this problem may be to use the change of base formula:
\(\Large \log_{16}32 = \frac{\log_{2}32}{\log_216} = \frac 54 \)

Answer 7

oh

Answer 8

So the left hand side is 5/4

5/4 = x + 5
x = 5/4 - 5 = (5-20)/4 = -15/4 = -3 & 3/4

Answer 9

so the answer is -3 3/4 or 5/4

Answer 10

No the answer is -3 3/4
solving by two different methods.

Answer 11

ohhh