Question

PLEASE I BEG YOU, HELP ME, I'M DESPARTE

What is the solution to the equation

2(3^x+1)+8=108???

Answer 1

i'll try :)

is it like this \(\sf 2(3^x+1)+8=108 \) or \(\sf 2(3^{x+1})+8=108 \)

Answer 2

yes that's the quesion

Answer 3

\[2\times 3^{x+1}+8=108\] subtract \(8\) first and you have
\[2\times 3^{x+1}=100\] then divide by 2 and get
\[3^{x+1}=50\]

Answer 4

from there it depends on what kind of answer you are looking for
if you want a numerical answer, use the change of base formula
\[x+1=\frac{\ln(50)}{\ln(3)}\] then subtract 1 and use a calculator

Answer 5

omg, thank-you so very much

Answer 6

wait hold on, actually why did you put ln 50 over ln 3???

Answer 7

yw
the final answer will be
\[x=\frac{\ln(50)}{\ln(3)}-1\]

Answer 8

why not just 50/3???

Answer 9

ok lets go slow a little

Answer 10

this is called the "change of base" formula
\[b^x=A\iff x=\frac{\ln(A)}{\ln(b)}\]

Answer 11

you have
\[3^{x+1}=50\] so
\[x+1=\frac{\ln(50)}{\ln(3)}\]

Answer 12

clear that up a little? i can show you another example if you like

Answer 13

no it's fine, thanks

Answer 14

lets go ahead and find the number
http://www.wolframalpha.com/input/?i=ln%2850%29%2Fln%283%29-1

Answer 15

actually that's all there is, but thanks

Answer 16

of course since we are going to end up with a calculator anyways, lets see if the answer is right
http://www.wolframalpha.com/input/?i=2*3^%28x%2B1%29%2B8%3D108

Answer 17

i'm just confused.. the question says: 2(3^x+1)+8=108,
not 2*3^(x+1)+8=108 ?

so it means it should be
\(\sf 2(3^x+1)+8=108\\2(3^x+1)=100\\3^x+1=50\\3^x=49\)

then apply the change of base...? @misty1212