Question

What is the solution to the equation 21^(x+3)=14? I need the answer in decimal form.

Answer 1

this question belongs to logarithm topic, right ??

Answer 2

right

Answer 3

log(14)/log(21) = x+3
(log(14)/log(21)-3 = x

Answer 4

(log(14)/log(21)) - 3 = x\
sorry forgot the parenthesis

Answer 5

first step will be to take log on both sides :)

Answer 6

then use the property
\(\Large \log a^b = b\log a\)

Answer 7

yeah, I got that, but all my answers are in approximate decimal form and I don't know how to get my equation to decimal form.

Answer 8

so, whats the last step you're stuck at ?
you got this ?
\(x = \log 14/\log 21 -3 \)
?

Answer 9

yeah, I just need it in decimal form

Answer 10

21^(x+3)=14

Put ln both sides

ln21^(x+3)=ln14

Put down the exponent.

(x+3)ln(21)=ln(14)

divide both sides by ln(21)

x+3=(ln14)/ln(21)

subtract both side by 3

x=(ln14)/ln(21)-3

x=0.867-3
x=-2.13

Answer 11

there you go ^
or you could have just used a calculator or even google :P

Answer 12

wow, awesome! thank you guys so much!

Answer 13

I like learning how to do things better than just getting the answer

Answer 14

thats a pretty cool way of learning, i am glad :)

Answer 15

Anytime.