Home
Class 12
MATHS
Find the number of solutions of equation...

Find the number of solutions of equation `(2x-3)2^x=1`

Text Solution

Verified by Experts

We have ` (2x - 3) 2^(x) = 1`
` or 2x-3 = 2^(-x) `
To find the number of roots of the above equation, we need to find the number of points of intersection of ` y = 2x - 3 and y = 2^(-x)`.
The graphs of functions are as shown in the following figure.

From the figure, graphs intersect at only one point.
Hence, there is only one solution of the given equation.
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 1.7|1 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 1.8|1 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 1.5|1 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE PUBLICATION|Exercise Subjective Type|9 Videos

  • MATHMETICAL REASONING

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

Similar Questions

Explore conceptually related problems

Find the number of solutions of equation 2^x+3^x+4^x-5^x=0

Find the number of solutions of the equation x^3+2x^2+5x+2cosx=0 in [0,2pi]

Consider the equation 2/x+5/y=1/3w h e r ex ,y in Ndot Find the number of solutions of the equation.

Find the number of solution to equation (log)_2(x+5)=6-x :

Find the number of solution to the equation x^(2)tanx=1,x in [0,2pi].

The graph of the function y=f(x) is shown. Find the number of solutions to the equation ||f(x)|-1|=(1)/(2) .

Find the number of solutions of the equation sinx=x^(2)+x+1.

Find the number of solution of the equation abs(sin x) = sin x + 3 if x in [0 , 2pi]

Find the number of solutions of the equation 3tanx+x^3=2 when x in (0,pi/4)

Show that the number of solutions of equations |x|^(2)-3|x|+2=0 is 4.

CENGAGE PUBLICATION-LOGARITHM AND ITS PROPERTIES-ILLUSTRATION 1.6
  1. Find the number of solutions of equation (2x-3)2^x=1

    Text Solution

    |