Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation sin(x)=1
-
Equation x^2-x-20=0
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Equation log(x)=0
- Equation ctg((x-pi)/4)-1=0
- Express {x} in terms of y where:
- 16*x+7*y=8
- 17*x-11*y=2
- -16*x-7*y=-5
- -1*x-7*y=5
-
Identical expressions
- logx27= three
- logarithm of x27 equally 3
- logarithm of x27 equally three
-
Similar expressions
- logx(27)x=2,5
- logx^2(7-x)=5
logx27=3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$27 \log{\left(x \right)} = 3$$
$$27 \log{\left(x \right)} = 3$$
Let's divide both parts of the equation by the multiplier of log =27
$$\log{\left(x \right)} = \frac{1}{9}$$
This equation is of the form:
By definition log
then
$$x = e^{\frac{3}{27}}$$
simplify
$$x = e^{\frac{1}{9}}$$
$$27 \log{\left(x \right)} = 3$$
$$27 \log{\left(x \right)} = 3$$
Let's divide both parts of the equation by the multiplier of log =27
$$\log{\left(x \right)} = \frac{1}{9}$$
This equation is of the form:
log(v)=p
By definition log
v=e^p
then
$$x = e^{\frac{3}{27}}$$
simplify
$$x = e^{\frac{1}{9}}$$
Sum and product of roots
[src]
sum
1/9 e
$$e^{\frac{1}{9}}$$
=
1/9 e
$$e^{\frac{1}{9}}$$
product
1/9 e
$$e^{\frac{1}{9}}$$
=
1/9 e
$$e^{\frac{1}{9}}$$
exp(1/9)