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magepker728
 2 years ago
1help step by step please on how to do this
5^x=4^x+1
magepker728
 2 years ago
1help step by step please on how to do this 5^x=4^x+1

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JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.1Well, clearly x = 1 is a solution, yes?

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.1Did you mean: 5^x=4^(x+1)

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.1The you could also write :\[5^x=4^{x+1} \Leftrightarrow 5^x=4^x \cdot 4^1 \]

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.1yes to \[ 5^x = 4^{x+1} \] ?

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.1Now you can divide by 4^x

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.1And use \[\frac{ a^x }{ b^x }=\left( \frac{ a }{ b } \right)^x\]

magepker728
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1359924788627:dw

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.1Alternatively, take the natural log of both sides and you have \[ \ln 5^x = \ln 4^{x+1} \] \[ x \ln 5 = (x+1) \ln 4 \] Now solve for x.

magepker728
 2 years ago
Best ResponseYou've already chosen the best response.0@JamesJ that is where my problem is solvinf for that x :D

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.1So subtracting ln 4 . x from both sides, we have \[ (\ln 5  \ln 4)x = \ln 4 \] Yes? Now take it from there ...

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.1I did the following: \[5^x=4^x \cdot 4 \Leftrightarrow \left( \frac{ 5 }{ 4 } \right)^x=4\]\[x=\log_{\frac{ 5 }{ 4 }} 4=\frac{ \ln4 }{ \ln \frac{ 5 }{ 4 } }=\frac{ \ln 4 }{ \ln5\ln4 }\]

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.1@JamesJ: sorry, didn't mean to give it away...

magepker728
 2 years ago
Best ResponseYou've already chosen the best response.0thank you every1 for ur help
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