Exponential Equations

[lexieaj]

Hi!

Have a couple problems I get stuck o because the variable "x" is on both sides of the equation as an exponent. See problem below:

10^(1-x)= 6^x
e
My steps until i get stuck are:

log 10^(1-x)= 6^x
(1-x) log 10 = x log 6
{(1-x) log 10}/log 6 = x

at this point I am stuck, and have more problems similar to this. Can anyone enlighten me? Thanks so much!

 

[arthur ohlsten]

10^(1-x)=6^x take log to base 10
1-x=x log 6
1=x[1+log6]
x=1/[1+log6] answer
====================================================
I suggest you do it using log to base 6

Arthur

 

[lexieaj]

arthur,
This is lexie regarding your response to exponential equations. You said take it to log 10, but then at the end you said base 6. Can you explain this further? Thanks

 

[Mrspi]

Hi!

Have a couple problems I get stuck o because the variable "x" is on both sides of the equation as an exponent. See problem below:

10^(1-x)= 6^x
e
My steps until i get stuck are:

log 10^(1-x)= 6^x<---you need to take the log of BOTH sides:
log 10^(1 - x) = log (6^x)
(1-x) log 10 = x log 6<---log 10^(1 - x) is just 1 - x
{(1-x) log 10}/log 6 = x

at this point I am stuck, and have more problems similar to this. Can anyone enlighten me? Thanks so much!

Ok...

1 - x = log 6^x
1 - x = x log 6

Get all of the terms containing x on one side of the equals sign:

1 = x + x log 6

Remove a common factor of x from both terms on the right side:

1 = x(1 + log 6)

Divide both sides by (1 + log 6):

1 / [1 + log 6) = x