How to solve for x:27^x=9^x-4

Question

asked Mar 14, 2023 72.7k views

1 Answer

Iryna · Answer 1 · 2023-03-21T06:48:51+0000

In order to solve for x, we will need to apply a logarithm in both sides of the equation.

First, let's remember some properties of logarithm expressions:

$\begin{gathered} \log (a^b)=b\cdot\log (a) \\ \log (a)+\log (b)=\log (a\cdot b) \\ \log (a)-\log (b)=\log ((a)/(b)) \end{gathered}$

So we have:

$\begin{gathered} 27^x=9^x-4 \\ (3^3)^x=(3^2)^x-4 \\ (3^x)^3=(3^x)^2-4 \end{gathered}$

Let's substitute 3^x by y, then let's solve for y: