anonymous
  • anonymous
1help step by step please on how to do this 5^x=4^x+1
Mathematics
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anonymous
  • anonymous
1help step by step please on how to do this 5^x=4^x+1
Mathematics
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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JamesJ
  • JamesJ
Well, clearly x = 1 is a solution, yes?
ZeHanz
  • ZeHanz
Did you mean: 5^x=4^(x+1)
anonymous
  • anonymous
yes

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ZeHanz
  • ZeHanz
The you could also write :\[5^x=4^{x+1} \Leftrightarrow 5^x=4^x \cdot 4^1 \]
JamesJ
  • JamesJ
yes to \[ 5^x = 4^{x+1} \] ?
anonymous
  • anonymous
ZeHanz
  • ZeHanz
Now you can divide by 4^x
ZeHanz
  • ZeHanz
And use \[\frac{ a^x }{ b^x }=\left( \frac{ a }{ b } \right)^x\]
anonymous
  • anonymous
|dw:1359924788627:dw|
JamesJ
  • JamesJ
Alternatively, 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.
anonymous
  • anonymous
i got to this part
anonymous
  • anonymous
@JamesJ that is where my problem is solvinf for that x :D
JamesJ
  • JamesJ
So subtracting ln 4 . x from both sides, we have \[ (\ln 5 - \ln 4)x = \ln 4 \] Yes? Now take it from there ...
ZeHanz
  • ZeHanz
I 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
  • ZeHanz
@JamesJ: sorry, didn't mean to give it away...
anonymous
  • anonymous
thank you every1 for ur help

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