Solve the equation,
9^4x-3=27^5x

Question

Solve the equation,
9^4x-3=27^5x

imqwerty · Answer

$$9^4x-3=27^5x$$ is this ur ques?

michele_laino · Answer

I think it is:
$$\Large  {9^{\left( {4x - 3} \right)}} = {27^{5x}}$$
@imqwerty

imqwerty · Answer

ah yes :)

anonymous · Answer

In the first part, the x-3 is in with the power, and in the second part the x is also in with the power.

Yes, Michele_Laino that's right

imqwerty · Answer

$$9^{4x-3}=27^{5x}$$$$3^{2(4x-3)}=3^{3(5x)}$$when bases are same powers are equal
so
2(4x-3)=5x

can u get x from here?

anonymous · Answer

So now do you just solve for x?

michele_laino · Answer

yes!

anonymous · Answer

Okay.

anonymous · Answer

Does x=2?

michele_laino · Answer

hint:
we can simplify the equation above like below:
$$\Large   \begin{gathered}
  2\left( {4x - 3} \right) = 3\left( {5x} \right) \hfill \
  8x - 6 = 15x \hfill \ 
\end{gathered} $$

aaronandyson · Answer

:)

anonymous · Answer

So the answer is -6/7?

michele_laino · Answer

correct!

anonymous · Answer

Okay, so question with the hint that you gave me where did you get the 3(5x) from?

anonymous · Answer

Okay, so question with the hint that you gave me where did you get the 3(5x) from?

michele_laino · Answer

since I can write this:
$$\huge  {27^{5x}} = {\left( {{3^3}} \right)^{5x}} = {3^{\left( {3 \cdot 5x} \right)}}$$

anonymous · Answer

Ohh, okay. Got it now. Thanks so much!!

michele_laino · Answer

:)