# Solving an exponential equation with two unknowns

• Apr 21st 2009, 07:28 PM
math123456
Solving an exponential equation with two unknowns
solve the following system:

2^(x+3y) = 128
• Apr 21st 2009, 07:31 PM
mr fantastic
Quote:

Originally Posted by math123456
solve the following system:

2^(x+3y) = 128

Start by solving x + 3y = 7.
• Apr 21st 2009, 07:33 PM
IAmLegendToo
Not 100% sure here, but.

To solve for y.

Rewrite 128 as 2 to the something power, which is:

2 to the 7th power.

Set x+3y equal to 7.

x+3y = 7
3y = -x + 7
y = -(x-7)/3

Same for x, except solve x+3y = 7 for x.
x = -3y + 7

I believe this is how it's done.
• Apr 21st 2009, 08:00 PM
pickslides
Quote:

Originally Posted by IAmLegendToo
Not 100% sure here, but.

To solve for y.

Rewrite 128 as 2 to the something power, which is:

2 to the 7th power.

Set x+3y equal to 7.

x+3y = 7
3y = -x + 7
y = -(x-7)/3

Same for x, except solve x+3y = 7 for x.
x = -3y + 7

I believe this is how it's done.

Because there are 2 variables in the one equation there will be infinite solutions that lie on the line

$\displaystyle y =\frac{-x}{3}+=\frac{7}{3}$
• Apr 22nd 2009, 10:55 AM
HallsofIvy
You said, in your first post, "Solve the following system" (my emphasis). You did not give a system. What does the problem really say?