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log4(x-10)=log45 equation

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Numerical solution:

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The solution

You have entered [src] 
log(x - 10)          
----------- = log(45)
   log(4)
log⁡(x−10)log⁡(4)=log⁡(45)\frac{\log{\left(x - 10 \right)}}{\log{\left(4 \right)}} = \log{\left(45 \right)}
Simplify
Detail solution
Given the equation
log⁡(x−10)log⁡(4)=log⁡(45)\frac{\log{\left(x - 10 \right)}}{\log{\left(4 \right)}} = \log{\left(45 \right)}
log⁡(x−10)log⁡(4)=log⁡(45)\frac{\log{\left(x - 10 \right)}}{\log{\left(4 \right)}} = \log{\left(45 \right)}
Let's divide both parts of the equation by the multiplier of log =1/log(4)
log⁡(x−10)=log⁡(4)log⁡(45)\log{\left(x - 10 \right)} = \log{\left(4 \right)} \log{\left(45 \right)}
This equation is of the form:
log(v)=p

By definition log
v=e^p

then
x−10=elog⁡(45)1log⁡(4)x - 10 = e^{\frac{\log{\left(45 \right)}}{\frac{1}{\log{\left(4 \right)}}}}
simplify
x−10=elog⁡(4)log⁡(45)x - 10 = e^{\log{\left(4 \right)} \log{\left(45 \right)}}
x=10+elog⁡(4)log⁡(45)x = 10 + e^{\log{\left(4 \right)} \log{\left(45 \right)}}
The graph
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Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
            log(4)
x1 = 10 + 45
x1=10+45log⁡(4)x_{1} = 10 + 45^{\log{\left(4 \right)}} 
x1 = 10 + 45^log(4)
Sum and product of roots [src] 
sum
       log(4)
10 + 45
10+45log⁡(4)10 + 45^{\log{\left(4 \right)}} 
=
       log(4)
10 + 45
10+45log⁡(4)10 + 45^{\log{\left(4 \right)}} 
product
       log(4)
10 + 45
10+45log⁡(4)10 + 45^{\log{\left(4 \right)}} 
=
       log(4)
10 + 45
10+45log⁡(4)10 + 45^{\log{\left(4 \right)}} 
10 + 45^log(4)
Numerical answer [src] 
x1 = 205.811946936753
x1 = 205.811946936753
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