Mister Exam
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Identical expressions
- log five (5-x)=log53
- logarithm of 5(5 minus x) equally logarithm of 53
- logarithm of five (5 minus x) equally logarithm of 53
- log55-x=log53
-
Similar expressions
- log5(3-2*x)=log5^-1(x)
- log5(3-2x)=log1/5x
- log5(5+x)=log53
- log5(3x-2)=log5*7
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log5(5-x)=log53 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
log(5 - x) ---------- = log(53) log(5)
$$\frac{\log{\left(5 - x \right)}}{\log{\left(5 \right)}} = \log{\left(53 \right)}$$
Detail solution
Given the equation
$$\frac{\log{\left(5 - x \right)}}{\log{\left(5 \right)}} = \log{\left(53 \right)}$$
$$\frac{\log{\left(5 - x \right)}}{\log{\left(5 \right)}} = \log{\left(53 \right)}$$
Let's divide both parts of the equation by the multiplier of log =1/log(5)
$$\log{\left(5 - x \right)} = \log{\left(5 \right)} \log{\left(53 \right)}$$
This equation is of the form:
By definition log
then
$$5 - x = e^{\frac{\log{\left(53 \right)}}{\frac{1}{\log{\left(5 \right)}}}}$$
simplify
$$5 - x = e^{\log{\left(5 \right)} \log{\left(53 \right)}}$$
$$- x = -5 + e^{\log{\left(5 \right)} \log{\left(53 \right)}}$$
$$x = 5 - e^{\log{\left(5 \right)} \log{\left(53 \right)}}$$
$$\frac{\log{\left(5 - x \right)}}{\log{\left(5 \right)}} = \log{\left(53 \right)}$$
$$\frac{\log{\left(5 - x \right)}}{\log{\left(5 \right)}} = \log{\left(53 \right)}$$
Let's divide both parts of the equation by the multiplier of log =1/log(5)
$$\log{\left(5 - x \right)} = \log{\left(5 \right)} \log{\left(53 \right)}$$
This equation is of the form:
log(v)=p
By definition log
v=e^p
then
$$5 - x = e^{\frac{\log{\left(53 \right)}}{\frac{1}{\log{\left(5 \right)}}}}$$
simplify
$$5 - x = e^{\log{\left(5 \right)} \log{\left(53 \right)}}$$
$$- x = -5 + e^{\log{\left(5 \right)} \log{\left(53 \right)}}$$
$$x = 5 - e^{\log{\left(5 \right)} \log{\left(53 \right)}}$$
Sum and product of roots
[src]
sum
log(5) 5 - 53
$$5 - 53^{\log{\left(5 \right)}}$$
=
log(5) 5 - 53
$$5 - 53^{\log{\left(5 \right)}}$$
product
log(5) 5 - 53
$$5 - 53^{\log{\left(5 \right)}}$$
=
log(5) 5 - 53
$$5 - 53^{\log{\left(5 \right)}}$$
5 - 53^log(5)
Rapid solution
[src]
log(5) x1 = 5 - 53
$$x_{1} = 5 - 53^{\log{\left(5 \right)}}$$
x1 = 5 - 53^log(5)