SOLUTION: Please explain how to solve: {{{ e^(x)-8e^(-x)=7 }}} and solve for x (exact answer) {{{ 10^(10-x)=16^(x) }}} Thank you

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please explain how to solve: {{{ e^(x)-8e^(-x)=7 }}} and solve for x (exact answer) {{{ 10^(10-x)=16^(x) }}} Thank you      Log On


   



Question 959160: Please explain how to solve:
+e%5E%28x%29-8e%5E%28-x%29=7+

and

solve for x (exact answer)
+10%5E%2810-x%29=16%5E%28x%29+

Thank you

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
e%5E%28x%29-8e%5E%28-x%29=7

%28e%5E%28x%29-8e%5E%28-x%29%29e%5Ex=7%2Ae%5Ex

e%5E%282x%29-8=7e%5Ex

e%5E%282x%29-7e%5Ex-8=0
Still not finished solving, but the equation is in quadratic form, and you can solve for e%5Ex.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Please explain how to solve:
+e%5E%28x%29-8e%5E%28-x%29=7+

and

solve for x (exact answer)
+10%5E%2810-x%29=16%5E%28x%29+

Thank you
e%5Ex+-+8e%5E%28-+x%29+=+7
e%5Ex+-+8e%5E%28-+x%29+-+7+=+0
e%5Ex+-+8%281%2Fe%5Ex%29+-+7+=+0
e%5Ex+-+%288%2Fe%5Ex%29+-+7+=+0
e%5Ex+%2A+e%5Ex+-+8+-+7e%5Ex+=+0 --------- Multiplying by LCD, e%5Ex
e%5E%282x%29+-+7e%5Ex+-+8+=+0
%28e%5Ex+-+8%29%28e%5Ex+%2B+1%29+=+0
e%5Ex+-+8+=+0 OR e%5Ex+=+-+1 (ignore)
e%5Ex+=+8 ----- Exponential form
ln 8 = x --- Logarithmic form
highlight_green%28x+=+2.079442%29
10%5E%2810+-+x%29+=+16%5Ex ----------- Exponential form
log+10%5E%2810+-+x%29+=+log+16%5Ex ----- Taking log of both sides
10 - x (log 10) = x (log 16)
(10 – x) * 1 = x log 16
10 – x = x log 16
10 = (x log 16) + x
10 = x[(log 16) + 1)]
highlight_green%28x+=+10%2F%28%28log+16%29+%2B+1%29%29