SOLUTION: Hi, I really don't understand why you have to change the ln to e while solving this equation for x. Thank you. ln4x=2.1

Question 1049524: Hi, I really don't understand why you have to change the ln to e while solving this equation for x. Thank you.
ln4x=2.1

Answer by Natolino1983(23) (Show Source): You can put this solution on YOUR website!
Because, both functions (lnx) and exp(x)) are injective. That means that ln(a) = ln(b) only if a = b.
Also ln(x) in the inverse fuction of exp(x), so you can always solve an expression with one function using its inverse.
you don't know the value of 4x (becuade that's the question), but you apply the inverse function on both sides and solve the linear equation that appears.
4x =exp(2,1)
x = exp(2,1)/4

x= 2,041542478
Follow me on twitter for more @natolino_
RELATED QUESTIONS
Solve x in terms of y. Question: y = (e^x + e^-x)/(e^x - e^-x) Answer: x= 1/2 ln (answered by Edwin McCravy)

I have been working on this math problem for a while now and I don't understand how to do (answered by lwsshak3)

i have to graph y=x(1+x)^2 but what i don"t understand is why is it when you foil it in... (answered by Fombitz)

hi, i need your help please... i don't know how to answer these questions because i can't (answered by Theo,ikleyn,greenestamps,n2)

HELP! im not sure how to go about solving these 2 simple problems! 1) ln(5x) + ln(9) = (answered by Fombitz)

log6 (3) + log5 (2) is equivalent to A 0 B ln(2) * ln (6) C 1 / ln(6) D ln(2) / ln (answered by rapaljer)

Hello! I am clueless where to go from here: Consider the following equation: ln(x+7)... (answered by Fombitz)

I need to understand the steps in solving this equation by (1)solving for x and (2)... (answered by stanbon)

Morning, Please could somebody possible help with this Right its been a while since (answered by Fombitz)