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2log16(2x−5)=2 equation

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Numerical solution:

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The solution

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  log(2*x - 5)    
2*------------ = 2
    log(16)
2log⁡(2x−5)log⁡(16)=22 \frac{\log{\left(2 x - 5 \right)}}{\log{\left(16 \right)}} = 2
Simplify
Detail solution
Given the equation
2log⁡(2x−5)log⁡(16)=22 \frac{\log{\left(2 x - 5 \right)}}{\log{\left(16 \right)}} = 2
2log⁡(2x−5)log⁡(16)=2\frac{2 \log{\left(2 x - 5 \right)}}{\log{\left(16 \right)}} = 2
Let's divide both parts of the equation by the multiplier of log =2/log(16)
log⁡(2x−5)=log⁡(16)\log{\left(2 x - 5 \right)} = \log{\left(16 \right)}
This equation is of the form:
log(v)=p

By definition log
v=e^p

then
2x−5=e221log⁡(16)2 x - 5 = e^{\frac{2}{2 \frac{1}{\log{\left(16 \right)}}}}
simplify
2x−5=162 x - 5 = 16
2x=212 x = 21
x=212x = \frac{21}{2}
The graph
2.55.07.510.012.515.017.520.022.525.027.530.0-1010
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 21/2
x1=212x_{1} = \frac{21}{2} 
x1 = 21/2
Sum and product of roots [src] 
sum
21/2
212\frac{21}{2} 
=
21/2
212\frac{21}{2} 
product
21/2
212\frac{21}{2} 
=
21/2
212\frac{21}{2} 
21/2
Numerical answer [src] 
x1 = 10.5
x1 = 10.5
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