Question

find the value of x in the exponential equation 2^[(2/3)x+1] – 3 . 2^[(1/3)x] – 20 = 0 I'm having a hard time here.. can somebody help me??

Answer 1

the equation is like this right ??
\[\left( 2^\frac{ 2x+3 }{ 3 }-3 \right)\left( 2^\frac{ x }{3 } -30\right)=0\]

Answer 2

-20*

Answer 3

thanks:D

Answer 4

that was not the answer ! I was cheking from the question

Answer 5

im just thanking because ive waited hours before somebody entertains my question

Answer 6

ok lets do it together ,first lets analyze brackets
\[2^\frac{ x-3 }{ 3 } -(2^\frac{ 2x-1 }{ 3} \times 5)-(2^\frac{ x }{ 3 }\times3)+60\]

Answer 7

did you expand it? im bit confused

Answer 8

yeb , I did , whats make u confuse ?

Answer 9

mmm Im going to sol the question in different way

Answer 10

\[\left( 2^\frac{ 2x-3 }{ 3 } -3\right)\left( 2^\frac{ x }{ 3 } -20\right)=0\]

Answer 11

assume
\[y=2^\frac{ x }{ 3 }\]
\[y^2=2^\frac{ 2x }{ 3 }\]
the equation convert to
\[(2y^2-3)(y-20)=0\]
case one
\[y=20 \]
when y=20
\[2^\frac{ x }{ 3 }=20\]
case two
\[y^2=\frac{ 3 }{ 2 } ,2^\frac{ 2x }{ 3 }=\frac{ 3 }{ 2 }\]

Answer 12

\[the equation is like this 2^\left( 2/3)(x+1 \right)-3\times2^\left( 1/3)(x \right)-20=0\]

Answer 13

now its better

Answer 14

like this ?
\[2^\frac{ 2x+2 }{ 3 }-3\times2^\frac{ x }{ 3 }-20=0\]
or this ?
\[2^\frac{ 2x+3 }{ 3 }-3\times2^\frac{ x }{ 3 }-20=0\]

Answer 15

the first one

Answer 16

ok assume
\[y=2^\frac{ x }{3 }\]
\[y^2=\frac{ 2x }{ 3 }\]
the equation would be
\[2^\frac{ 2 }{ 3 }\times y^2-3y-20=0\]
solve for y using the general law

Answer 17

where did the y came from?
i thought we're finding for x?

Answer 18

I assumed \[y=2^\frac{ x }{ 3}\]

Answer 19

oh ok..

Answer 20

so finally y=6 or 0
when y=6
\[2^\frac{ x }{ 3 }=6\]
or
\[2^\frac{ x }{ 3 }=0\]
is that ok untill now ??

Answer 21

yes.. keep going

Answer 22

\[x=\ln \sqrt[3]{6},for.base2\rightarrow or, x=\ln 0, for.base 2\]

Answer 23

uhmm i remember the process thanks for refreshing it ... im very glad that you lend me your time.. i better get going because my mom just scolded me earlier.. i hope you'll teach me again next time :D

Answer 24

any thing u need I'd be happy if I help u :)