Solve: 5^(2x-3)=7^(x+1)

Question

callisto · Answer

Have you learnt logarithm yet?

anonymous · Answer

yes. can you just check my answer?

callisto · Answer

Okay.

anonymous · Answer

log875/(log25-log7)

callisto · Answer

I got the same answer as yours.

anonymous · Answer

okay thanks. actually can you show me how you did that. I took long time to figure this out and I want to know if there is an easier way

callisto · Answer

I guess more or less the same as you did..
$$5^{2x-3}=7^{x+1}$$$$(2x-3)\log5=(x+1)\log7$$$$2x\log5-3\log5=x\log7+\log7$$$$x(2\log5-\log7)=\log7+3\log5$$$$x=\frac{\log7+3\log5}{(2\log5-\log7)}=\frac{\log(7\times5^3)}{\log25-\log7}$$

anonymous · Answer

I did not it that way but I guess that works too

callisto · Answer

How did you do it?

anonymous · Answer

$$5 ^{2x-3}=7^{x+1}$$$$\frac{ 5^{2x} }{ 5^{3} }=7^{x}*7$$$$5^{x}=7^{x}*875$$$$(\frac{ 25 }{ 7 })^{x}=875$$$$x=\log_{25/7}875=\frac{ \log875 }{ \log25-\log7 } $$

anonymous · Answer

it's so difficult to think of ways to solve math problems. The method always seems to escape me

anonymous · Answer

thanks for your help

callisto · Answer

Your method looks nice :)
I was taught to solve question in that way :(