Question

( I )expand the following numbers using

exponents. 1)623.98 2)2896.305

( II ) If 2 power x =1 then find the value of x

​

Answer 1

Answer:

2.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

Answer 2

Answer:

The required value of x is given by :

x = \frac{\ln 1.5}{\ln 6}x=

ln6

ln1.5