Solve in exact form
1) 3(2)^x = 18^(x-1)
2) 2(27)^x = 9^(x+1)
Can anyone help with any of these questions?
Take the natural log of both sides:
Use the multiplication identity: ln(ab) = ln(a) + ln(b)
Use the exponent identity:
Distribute the ln(18)
Put all the terms with x in them on one side by subtracting x*ln(2) from both sides:
Put all the terms without x in them on the other side by adding ln(18) to both sides:
Factor out an x:
Divide by the coefficient of x, which is [ln(18)-ln(2)]
Use additive identity of logarithms to see that
Use subtraction identity to see that
Now you've solved for x,
an alternate approach. (i originally thought it could be done without logs, so i tried simplifying to equate like powers, but i had to end up using them at the end)
.........2^x is never zero so we can divide by it
here is where i said, "Oh, darn it! I need logs!"
as angel.white said
Then manipulate the equation using what you know about logs.
Now no more x's are exponents, so you can just rearrange this equation using more elementary techniques to isolate the x.
Thanks so much!!! and yeah i get it now, but i did the second one and i got a different answer, i actually got
log(2/9) / log(1/3) = 1.369
and when i substitute it back in, it worked... but i'll compare answers with someone tomorrow...
but thanks so much for helping