find the value of x in 2 power x=1
Answers
Answer:
The required value of x is given by :
x = \frac{\ln 1.5}{\ln 6}x=
ln6
ln1.5
Step-by-step explanation:
\begin{gathered}2^{x+1}=3^{1-x}\\\\\text{Taking natural log on both the sides}\\\\\implies (x+1)\ln 2=(1-x)\ln 3\\\\\implies x\ln 2+ \ln 2=\ln 3-x\ln 3\\\\\implies x\ln 2+x\ln 3=\ln 3-\ln 2\\\\\implies x(\ln 2 +\ln 3) = \ln 3-\ln 2\\\\\implies x\ln 6=\ln 1.5\\\\\implies x = \frac{\ln 1.5}{\ln 6}\end{gathered}
2
x+1
=3
1−x
Taking natural log on both the sides
⟹(x+1)ln2=(1−x)ln3
⟹xln2+ln2=ln3−xln3
⟹xln2+xln3=ln3−ln2
⟹x(ln2+ln3)=ln3−ln2
⟹xln6=ln1.5
⟹x=
ln6
ln1.5
Hence, The required value of x is given by :
x = \frac{\ln 1.5}{\ln 6}x=
ln6
ln1.5
I hope it will help you
thankyou
process 1 :
=> 2^x=1
=> 2^x=2⁰ [°•° anything to the power 0 is 1]
°•° bases are same
x=0
process 2 :
=> 2^x=1
=> 2^x=2⁰
taking log on both sides,
log 2^x = log 2⁰ => x log 2 = 0 log 2 => x = 0 log2/log2 => x = 0