Question

Without a calculator how do i solve log16^8=(x+1)
move to exponent form..

Answer 1

what is the base of the logarithm here?

Answer 2

16 @whpalmer4

Answer 3

so you have \[\log_{16}8 = x+1\]?

Answer 4

yes @whpalmer4

Answer 5

remember, if \[\log_b u = a\]then \[b^a = u\]

Answer 6

so it would be 16(x+1)=8

Answer 7

? @whpalmer4

Answer 8

Uh, put a "^" in there if you want to indicate an exponent

Answer 9

16^(x+1)=8

Answer 10

Do you mean \[16(x+1) = 8\]or\[16^{x+1} = 8\]

Answer 11

Right. So how can you solve that?

Answer 12

im not sure lol

Answer 13

16 and 8 are both powers of 2, aren't they?

Answer 14

yeah

Answer 15

what are they, expressed as powers of 2?

Answer 16

\(2^8 = 16\)?

Answer 17

2*2=4
2*2*2=8
2*2*2*2=16

Answer 18

okay

Answer 19

so \[16=2^4\] and \[8=2^3\]right?

Answer 20

yup

Answer 21

Okay, do you remember that \[(ab)^n = a^nb^n\]

Answer 22

yeah

Answer 23

Okay, so we can rewrite our equation as \[(2*2*2*2)^{x+1} = 2^3\]

Answer 24

got it

Answer 25

what's your final answer?

Answer 26

oh was that the final step before the answer?

Answer 27

yeah, you still want to find \(x\), right?

Answer 28

yeah but if i were to factor that again wouldnt it just give me the same equation as before "16^x+1=8"

Answer 29

no, use that property I just showed you:\[(ab)^n = a^nb^n\]

Answer 30

whats the little symbols next to this (ab)? say its tiny

Answer 31

oh, try this:
\[\huge (ab)^n = a^nb^n\]

Answer 32

Here, I'll just write it out for you:

\[\huge (2*2*2*2)^{x+1} = 2^3\]\[\huge 2^{x+1}2^{x+1}2^{x+1}2^{x+1} = 2^3\]

Answer 33

And remember that \[\huge x^nx^m = x^{n+m}\]

Answer 34

So that gives us \[\huge 2^{4(x+1)} = 2^{3}\]\[x=\]

Answer 35

i got -1/4 @whpalmer4

Answer 36

Very good!

Answer 37

Thank you so much, ill give you a medal :)

Answer 38

1000 medals and $3.50 gets you a cup of coffee at Starbucks :-)

Answer 39

interesting, how many medals do you have?

Answer 40

(they are always appreciated, even if worthless!)

Answer 41

2093, apparently. If you click on someone's name, the little window that pops up gives you a link to click to see their entire profile, which shows how many fans, how many medals, questions answered/asked, shoe size, etc.

Answer 42

You could also have solved the last bit of this problem by noticing that

\[(2^4)^{x+1} = 2^3\]Remember that \[(u^a)^b = u^{a*b}\]so we have \[2^{4*(x+1)} = 2^3\]

Answer 43

wow thats so awesome, and you just received another fan hehe thanks :)