solving exponential functions

Question

$(27^{x - 1})(3^x) = 9^{2x-3}$. I apologize if you do not understand the equation. I was unsure on how exactly to represent it correctly. I have gotten to the step in the equation where it is $3^{4x-3} = 3^{4x-6}$ and then you set the exponents equal to each other, so $4x-3=4x-6$ but my teacher did not explain what happens when the $x$'s cancel and they will clearly cancel in this equation. So if anyone can tell me what to do next, it would be greatly appreciated!

Is the upper-case X supposed to be read as a multiplication sign? — hmakholm left over Monica, Mar 23 '14 at 22:18
yes the capital X is supposed to represent multiplication and it is the second option where the 4x-3 is the exponent and 4x-6 is the exponent — Ila Isabelle, Mar 23 '14 at 22:26
and again, so sorry, I know it's confusing the way I typed it — Ila Isabelle, Mar 23 '14 at 22:26
Oh, I see. Is the original equation $27^{x-1}3^x = 9^{2x-3}$? It would really help with some parentheses -- usually an ^ for exponentiation binds much tighter than subtraction, so it looked like you've written $(27^x-1)3^x=9^{2x}-3$. — hmakholm left over Monica, Mar 23 '14 at 22:27

score 1 · Answer 1 · answered Mar 23 '14 at 22:22

1

After cancelling the $4x$ term from both sides, we find that $-3 = -6$, a contradiction. So the equation has no solution. That is, if you plot each side of the equation separately, then the curves won't intersect.

answered Mar 23 '14 at 22:22

Adriano

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solving exponential functions

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