SOLUTION: Hi, I'm having difficulty solving this equation. ln(2^(4x-1))=ln(8^(x+5))+logbase2(16^(1-2x)) (expressing the answer in terms of ln2) I simplified it until ln(2^(x-16))=4-8x W

Question 596631: Hi, I'm having difficulty solving this equation.
ln(2^(4x-1))=ln(8^(x+5))+logbase2(16^(1-2x))
(expressing the answer in terms of ln2)
I simplified it until
ln(2^(x-16))=4-8x
Where do I go from there?
Thanks
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

You have done a lot of the work already. Your equation:

is correct. The next step is to use a property of logarithms, , to move the exponent of the argument out in front:

Multiplying out the left side we get:

Next we gather all the terms with on in them on one side of the equation and the other terms on the other side. Adding 8x and 16ln(2) to each side we get:

Next we factor out x on the left side:

And last we divide both sides by (ln(2) + 8):

And since the fraction on the right will not simplify, we are finished!
RELATED QUESTIONS
"Rewrite the expression 3 ln(4) - 2 ( ln(10) - ln(2) ) in the form ln(x), a single... (answered by jim_thompson5910)

Solve: log base 4 (X) + Log base 8 (x) = 1 ln X/ln 4 + ln X/ln 8=1 2 ln X/2 ln 4 + ln... (answered by Fombitz)

Hi, I'm having difficulty solving this equation. 5^(3a)*4^(2a+1)-10^(3a+2)=0... (answered by scott8148)

How do i solve A=ln2 in terms of A ln(16) ln(square root of 2)... (answered by stanbon)

2. The first three terms of a geometric sequence are ln x^16, ln x^8, ln x^4, for x>0. (answered by Edwin McCravy)

Rewrite the expression 3 ln(2) - 2 ( ln(10) - ln(4) ) in the form ln(x), a single... (answered by stanbon,josmiceli)

Solve the exponential equation. Express the solution set in terms of natural logarithms. (answered by LinnW)

is the answer to 2^(x+1)=5^(1-2x) x=(ln 2+ln 5)/(ln... (answered by stanbon,KMST)

Ln(4x+1)=ln(2x+5) (answered by nerdybill)