# Math Help - how to solve 5^(x-1) – 5^(x+2) = 10?

1. ## how to solve 5^(x-1) – 5^(x+2) = 10?

Hi,
Can anyone tell me how to solve “x” for this equation: 5^(x-1) – 5^(x+2) = 10?
Thank you

2. Originally Posted by ycdfd
Hi,
Can anyone tell me how to solve “x” for this equation: 5^(x-1) – 5^(x+2) = 10?
Thank you
$5^{x-1} - 5^{x+2} = 10$

$5^{x-1} - 5^{x-1}\times 5^{3} = 10$

$5^{x-1} (1-125) = 10$

$5^{x-1} = \frac{-10}{124}$

Since $5 ^{anything} \ne \text { a negative number}$

Thus x has no values

3. Originally Posted by ycdfd
Hi,
Can anyone tell me how to solve “x” for this equation: 5^(x-1) – 5^(x+2) = 10?
Thank you
This equation doesn't have a real solution:

\begin{aligned}5^{x-1}-5^{x+2}=&10 \\ \frac15 \cdot 5^x-25 \cdot 5^x = &10 \\ -\frac{124}5 \cdot 5^x =& 10\\5^x=&-\frac{50}{124}\end{aligned}

A power with a positive base will never be negative.

Thus $x \notin \mathbb{R}$