Question

Hello- exponential equations! Have answers, need help with understanding! Thanks in advance.
Solve for x.
1) 3^(2x+1)*5(2x-1) = 42
2) 18^(2x+1) = 5*6^(2x+1)

Answer 1

ok so you can put Ln on both sides of the equation.. lets take equation number 2 for example :
Ln(18^(2x+1)) = Ln(5*6^(2x+1))
do you think you can continue ?

Answer 2

i'll try for a bit! just a sec
(2x+1)ln18 = (2x+1)ln(5*6)
is that right?

Answer 3

so far i mean

Answer 4

not quite ..
your left side is right
but look.. your right side should be :
Ln(5*6^(2x+1)) = Ln(5) + (2x+1)Ln(6)
Do you understand why ?

Answer 5

i see, 5*6^2x+1 .... (take ln) = ln5*ln6^2x+1 = ln5 + (2x+1)ln6

Answer 6

that already helps

Answer 7

ok, i'll try myself for a bit

Answer 8

wait .. writing : ln5*ln6^2x+1 isnt correct
see Ln(a*b) = Ln(a) + Ln(b)

Answer 9

ok keep going let me know if you need anything else

Answer 10

thanks so far

Answer 11

logs/ln follow distributive law with the coefficient right? (2x+1)ln6 can = (2x)ln6 + ln6

Answer 12

sure

Answer 13

ln(6) is just a number. Just like 2 only fancier (more digits)

Answer 14

im new to logarithms so its easy to forget that :-) it looks fancy

Answer 15

awesome, those tips helped, i get it now. i'll try the first one

Answer 16

Here is one way to solve the 2nd one:
(2x+1)*ln(18)= ln(5)+(2x+1)*ln(6)
subtract (2x+1)*ln(6) from both sides:
(2x+1)*ln(18) - (2x+1)*ln(6) = ln(5)
factor out (2x+1) on the left side:
(2x+1)*(ln(18)-ln(6))= ln(5)
and though not necessary, notice ln(18)- ln(6)= ln(18/6)= ln(3), so
2x+1= ln(5)/ln(3)
and x is
x= (ln(5)/ln(3) -1)* 0.5

Answer 17

that's exactly what i did too, cool
but was making the mistake of applying ln improperly as coolsector pointed out, then also forgetting that lnx is "just a number"
was making same mistakes with the first so it should go better

Answer 18

in being natural log

Answer 19

got both of them now! thank you both!