Question

How would I answer this question?

16^(x-1)=8

Answer 1

\[16^{x-1}=8\]

Answer 2

take logs.

(x - 1) ln 16 = ln 8

x - 1 = (ln 8) / (ln 16)

x = (ln 8) / (ln 16) + 1 = 1.75

Answer 3

All good now, @lunatic09 ?

Answer 4

Good luck to you in all of your studies! @lunatic09

Answer 5

Thank you so much, I get it!

Answer 6

Im gona have to look up log rules, aghhh haha. Thanks again!

Answer 7

uw! There is another "intuitive" way. You could look for a common root for a power and see "2". You would then take the 1/4 root of 16 to get "2" and then cube to get 8. That's a sort of short-cut.

Answer 8

Oh I see 17^.75 is the same thing as 2^3. My brain is so rusty after a month of school :(, thanks for the shortcut.

Answer 9

\[16^{x-1}=8\] can also be written as \[2^{4(x-1)}= 2^{3}\] since the bases are the same (2), equate the powers, that is
4(x-1)=3
4x-4=3
4x=3+4
4x=7
Hence, x= 7/4 or 1.75

Answer 10

Thanks for the other method sisi_m

Answer 11

So, [16^(1/4)]^3 -> 16^(3/4) = 8

Answer 12

And since the exponent is "x - 1" we have:

x - 1 = 3/4 -> x = 1.75

After a while, you'll do those in your head. Or go crazy first trying to!

Answer 13

My brain is definitely going crazy right now, but it time Ill definitely get better. Thanks for the shortcut!

Answer 14

So, that's actually 3 ways to do the problem. My 2 and also the method from sisi. Have a great day!

Answer 15

You're a life saver, you too!