Question

Solve: 7+15e^(1-3x)=10

Answer 1

So I am going to assume this is a logic problem.

15(2.718282$^{−3x+1}$) + 7 = 10

Subtract 7 from both sides.

15(2.718282$^{−3x+1}$) = 3

Divide both sides by 15.

$\frac{15(2.72.718282 ^{−3x+1}}{15} = \frac{3}{15}$

2.718282$^{-3x+1}$ = $\frac{1}{5}$

Now you solve for the exponent.

(Take log of both sides)

(−3x+1)*(log(2.718282))=log(1/5)

−3x+1 = $\frac{log \frac{1}{5} }{log(2.718282) }$

−3x+1=−1.609438

−3x+1−1=−1.609438−1(Subtract 1 from both sides)

−3x=−2.609438 (divide 3 on both sides)


Answer:

x = 0.869813

or...

Rounded Answer:
0.87