Question

Find x if (2/7)^2x = (7/2)^3x + 5.

Answer 1

need help

Answer 2

is the + 5 an exponent?

Answer 3

oooooooooooooooh

Answer 4

i thought it was
\[(\frac{2}{7})^{2x}=(\frac{7}{2})^{3x}+5\]

Answer 5

yes

Answer 6

^3x+5

Answer 7

but instead it is
\[(\frac{2}{7})^{2x}=(\frac{7}{2})^{3x+5}\]?

Answer 8

yes

Answer 9

that we can do! use logs

Answer 10

\[2x\ln(\frac{2}{7})=(3x+5)\ln(\frac{7}{2})\]

Answer 11

is step one. the algebra from here on in

Answer 12

what is In?

Answer 13

\[\ln(\frac{2}{7})\times 2x=\ln(\frac{7}{2})\times 3x+\ln(\frac{7}{2})\times 5\] etc.

Answer 14

what is ln?

Answer 15

well if you have never seen it this problem will not make sense unless you want to replace ln by log

Answer 16

do you know what log is?

Answer 17

i don't understand what is In?

Answer 18

do you know log? as in
\[f(x)=\log(x)\]?

Answer 19

ok

Answer 20

i am asking.

Answer 21

I don't know

Answer 22

\[\left(\frac{2}{7}\right)^{2x}=\left(\frac{7}{2}\right)^{3x+5}\]

\[\left(\frac{7}{2}\right)^{-2x}=\left(\frac{7}{2}\right)^{3x+5}\]

\[\Rightarrow -2x=3x+5\Rightarrow -5=5x\Rightarrow x=-1\]

Answer 23

yes it is

Answer 24

thanks