exponential equation in terms of natural logarithms. WHAT??

Question

2^x+8 = 3
Solve the exponential equation. Express the solution set in terms of natural logarithms.
How do I do this? Please show work.

Answer 1

2^x+8=3 There is no real solution solution.
2^x=-5
2 ln x=ln -5
ln x=.5 ln -5
x=√-5

Answer 2

Would it help to know that ln( 2^x) = x * ln( 2) ?

So you can use natural logarithms (ln) to solve your equation by taking the logarithm of both sides and bringing out the x per the definition above.

first

2^x + 8 = 3 becomes

2^x = -5 well now that won't work as ln is only defined for positive numbers. Now I am not sure what you should do.

Answer 3

first of all let me correct your problem
2^(x+8)=3
as no degree(or power) of a positive number can result in negative number

now take the natural (to the base 'e' ) log of equation [note=u can solve this by taking the log to any base, provided u know the logarithmic table for that base]---

ln[2^(x+8)]=ln3
(x+8)ln2=ln3 ln a^b = b ln a
x+8 = ln3/ln2
x= (ln3/ln2) - 8

the answer is
x = - 6.415

Answer 4

precise, to initiate, you're taking ln of both area (organic and organic log) so that you get ln4^(x+7)=ln6 utilizing the regulation of logarithms, you need to simplify the equation to: (x+7)ln4=ln6 simplify some extra... (divide by utilizing ln4 on both area) (x+7)=ln6/ln4 so, x= ln6/ln4 -7 :D