$\frac{25^x+125}{6}=5^{x+1}$ what is the value of $x$?

Question

It is just the title, $$\frac{25^x+125}{6}=5^{x+1}$$ What is the value of $x$?

Thanks.

Related : https://math.stackexchange.com/questions/1356236/what-is-the-solution-to-the-equation-9x-6x-2-cdot-4x-0 — lab bhattacharjee, May 23 '17 at 05:23

score 5 · Accepted Answer · answered May 23 '17 at 05:17

5

Hint:

$$25^x+125 = 6(5^{x+1})$$

$$5^{2x}-30(5^x)+125=0$$

Quadratic equation might be helpful.

answered May 23 '17 at 05:17

Siong Thye Goh

1

But how to eliminate 30? 125 is equal to $5^3$ – JamesB May 23 '17 at 05:24
1

I can replace $5^x$ for an $m$. – JamesB May 23 '17 at 05:29
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Then you get: $m^2-30m+125=0$. – Fred May 23 '17 at 05:46
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So (m-25)(m-5)=0. So m=25 or m=5. So $5^x = 25$ or $5^x=5$. Those are solvable aren't they. – fleablood May 23 '17 at 06:12

1 Answers1