Mister Exam

Other calculators

log2(2x-1)=2

log2(2x-1)=2 equation

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src] 
log(2*x - 1)    
------------ = 2
   log(2)
log⁡(2x−1)log⁡(2)=2\frac{\log{\left(2 x - 1 \right)}}{\log{\left(2 \right)}} = 2
Simplify
Detail solution
Given the equation
log⁡(2x−1)log⁡(2)=2\frac{\log{\left(2 x - 1 \right)}}{\log{\left(2 \right)}} = 2
log⁡(2x−1)log⁡(2)=2\frac{\log{\left(2 x - 1 \right)}}{\log{\left(2 \right)}} = 2
Let's divide both parts of the equation by the multiplier of log =1/log(2)
log⁡(2x−1)=2log⁡(2)\log{\left(2 x - 1 \right)} = 2 \log{\left(2 \right)}
This equation is of the form:
log(v)=p

By definition log
v=e^p

then
2x−1=e21log⁡(2)2 x - 1 = e^{\frac{2}{\frac{1}{\log{\left(2 \right)}}}}
simplify
2x−1=42 x - 1 = 4
2x=52 x = 5
x=52x = \frac{5}{2}
The graph
-10.0-7.5-5.0-2.50.02.55.07.510.012.515.017.5-2020
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 5/2
x1=52x_{1} = \frac{5}{2}
Simplify
Sum and product of roots [src] 
sum
0 + 5/2
0+520 + \frac{5}{2} 
=
5/2
52\frac{5}{2} 
product
1*5/2
1⋅521 \cdot \frac{5}{2} 
=
5/2
52\frac{5}{2} 
5/2
Numerical answer [src] 
x1 = 2.5
x1 = 2.5
The graph
log2(2x-1)=2 equation
    © Mister Exam – Calculator