Question

Show work and explain! Medal will be rewarded! :D

Answer 1

HAHA.

Answer 2

4^(x+2) = 48

Answer 3

What do you need to find, x?

Answer 4

Yes, can you show how the problem looks?

Answer 5

That looks a bit odd. I'll use the math thingy.

Answer 6

i like the math thingy

Answer 7

what math thingy @satellite73

Answer 8

\[b^x=A\iff x=\frac{\ln(A)}{\ln(b)}\]

Answer 9

\[4^{x+2} = 48\]\[\log_{4}48 = x +2 \]\[\frac{ \log 48 }{ \log4 } = x +2\]\[\frac{ \log 48 }{ \log 4 } - 2 = x\]

Answer 10

Lol @satellite73 I think it's called matlab?

Answer 11

\[4^{x+2} = 48\]

Answer 12

@Firejay5 What I did is I used logs to re express this equation, and then I isolated x and re expressed log base 4 48 to log 48/log 4 using the change of base rule.

Answer 13

or you can start with
\[(x+2)\ln(4)=\ln(48)\] and solve that for \(x\)
either way, you get the same answer

Answer 14

^yeah, that's a good idea too! That's actually a better way, nice @satellite73

Answer 15

in general if you have
\[b^x=y\] you can either write \(x=\log_b(y)\) but if you want an actual number (decimal) then you need \(b^x=y\iff x=\frac{\ln(y)}{\ln(b)}\)

Answer 16

Is there an easier way to do it?

Answer 17

as @thechocoluver445 said, this is sometimes called the "change of base" formula because
\[x=\log_b(y)=\frac{\ln(y)}{\ln(b)}\]

Answer 18

Yep. You can do that with any base log, \[\frac{ \ln x }{ \ln y } = \frac{ \log x }{ \log y } = \frac{ \log_{n} x }{ \log_{n} y }\]Any other would be correct, most of the time if you're using this formula you'll want to convert with natural log (ln) or base 10 log (just log) because those are the most common and are often their own calculator buttons.

Answer 19

My Algebra II book says a different way, can you solve it that way. It's example 5 on page 526. Here's the link: http://mrlarkins.com/algebra2/docs/chap10.pdf

Answer 20

Ahh I see. What they want you to do is rewrite the right side of the equation so that the bases are equal. This problem cannot be solved like example 5, however.
You must use logs in order to solve this function. See the first example on this page http://www.purplemath.com/modules/solvexpo2.htm for more clarification.