Help me solve this equation please

[OtZman]

I used to know how to do this, but I've forgotten. I need the answer for a marketing course assignment. When solving the equation, please explain briefly how you solve it so I understand. I want to know what x is here:

126.1*1.059^x = 360.4*1.032^x

Thanks!

[almostbusto]

log(xy) = log (x) + log (y)
log (a^x) = x log (a)

those two axioms are all you need.

[OtZman]

[ QUOTE ]
log(xy) = log (x) + log (y)
log (a^x) = x log (a)

those two axioms are all you need.

[/ QUOTE ]
I've forgotten how to use logarithms altogether, so if you could please help me solve it I'd be very thankful. /images/graemlins/smile.gif

[jstnrgrs]

[ QUOTE ]
I used to know how to do this, but I've forgotten. I need the answer for a marketing course assignment. When solving the equation, please explain briefly how you solve it so I understand. I want to know what x is here:

126.1*1.059^x = 360.4*1.032^x

Thanks!

[/ QUOTE ]

Take the log of both sides:

Log(126.1*1.059^x) = Log(360.4*1.032^x)
using the log axioms posted above
log(126.1)+log(1.059^x)=log(360.4)+log(1.032^x)
log(126.1)+log(1.059)*(x)=log(360.4)+log(1.032)*(x )
log(126.1)-log(360.4)=log(1.032)*(x)-log(1.059)*(x)
log(126.1)-log(360.4)=(log(1.032)-log(1.059))*(x)
(log(126.1)-log(360.4))/(log(1.032)-log(1.059))=x

plug the logs into your calculator, and you've got the answer.

[OtZman]

[ QUOTE ]
[ QUOTE ]
I used to know how to do this, but I've forgotten. I need the answer for a marketing course assignment. When solving the equation, please explain briefly how you solve it so I understand. I want to know what x is here:

126.1*1.059^x = 360.4*1.032^x

Thanks!

[/ QUOTE ]

Take the log of both sides:

Log(126.1*1.059^x) = Log(360.4*1.032^x)
using the log axioms posted above
log(126.1)+log(1.059^x)=log(360.4)+log(1.032^x)
log(126.1)+log(1.059)*(x)=log(360.4)+log(1.032)*(x )
log(126.1)-log(360.4)=log(1.032)*(x)-log(1.059)*(x)
log(126.1)-log(360.4)=(log(1.032)-log(1.059))*(x)
(log(126.1)-log(360.4))/(log(1.032)-log(1.059))=x

plug the logs into your calculator, and you've got the answer.

[/ QUOTE ]
Thanks a lot!

When I plug the whole thing into my calculator I get x= ~ -148. If I just enter the like this instead:
Y1= 126.1*1.059^x
Y2= 360.4*1.032^x

And plot the graphs, the intersect is at X= ~40.5.

Why's this?

This probably has a very simple explanation, but I'm just not seeing it right now. /images/graemlins/laugh.gif

[alphatmw]

i would guess parentheses errors.

[Borodog]

You are screwing up the calculator entry somehow.

[OtZman]

[ QUOTE ]
You are screwing up the calculator entry somehow.

[/ QUOTE ]
Ahh, there we are, you were right! Thanks!

Tricky with those parentheses. /images/graemlins/tongue.gif

2+2 rocks, not only can I get help with poker here, but also with what I should be doing instead of playing. /images/graemlins/tongue.gif

[BruceZ]

[ QUOTE ]
I used to know how to do this, but I've forgotten. I need the answer for a marketing course assignment. When solving the equation, please explain briefly how you solve it so I understand. I want to know what x is here:

126.1*1.059^x = 360.4*1.032^x

Thanks!

[/ QUOTE ]

Here is another way. Divide both sides by 1.032^x to get rid of the power of x on the right side:

126.1*(1.059/1.032)^x = 360.4

(1.059/1.032)^x = 360.4/126.1

Taking logs of both sides gives a simple algebraic equation:

x*log(1.059/1.032) = log(360.4/126.1)

x = log(360.4/126.1) / log(1.059/1.032)

x =~ 44.66

[OtZman]

[ QUOTE ]
[ QUOTE ]
I used to know how to do this, but I've forgotten. I need the answer for a marketing course assignment. When solving the equation, please explain briefly how you solve it so I understand. I want to know what x is here:

126.1*1.059^x = 360.4*1.032^x

Thanks!

[/ QUOTE ]

Here is another way. Divide both sides by 1.032^x to get rid of the power of x on the right side:

126.1*(1.059/1.032)^x = 360.4

(1.059/1.032)^x = 360.4/126.1

Taking logs of both sides gives a simple algebraic equation:

x*log(1.059/1.032) = log(360.4/126.1)

x = log(360.4/126.1) / log(1.059/1.032)

x =~ 44.66

[/ QUOTE ]
Sweet, thanks a lot! /images/graemlins/laugh.gif