Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2+6*x+9=0
-
Equation x^2+4=5x
- Equation (x+20)*(-x+10)=0
-
Equation cos(x)-sin(x)=1
- Express {x} in terms of y where:
- 20*x+18*y=-9
- 11*x-2*y=-9
- -13*x-10*y=5
- -7*x-19*y=-18
-
Identical expressions
- 3lg+ nineteen /3lg- one =2lgx+ one
- 3lg plus 19 divide by 3lg minus 1 equally 2lgx plus 1
- 3lg plus nineteen divide by 3lg minus one equally 2lgx plus one
- 3lg+19 divide by 3lg-1=2lgx+1
-
Similar expressions
- x/2=2*lg(x)+1
- 3lg+19/3lg-1=2lgx-1
- -lg(x+1)^2-2lg(x+1)=lg(x^2+6)-1
- Lgx-1/2lg(x-1/2)=lg(x+1/2)-1/2lg(x+1/8)
- 3lg+19/3lg+1=2lgx+1
- 3lg-19/3lg-1=2lgx+1
3lg+19/3lg-1=2lgx+1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
19*log(x)
3*log(x) + --------- - 1 = 2*log(x) + 1
3
$$\left(3 \log{\left(x \right)} + \frac{19 \log{\left(x \right)}}{3}\right) - 1 = 2 \log{\left(x \right)} + 1$$
Detail solution
Given the equation
$$\left(3 \log{\left(x \right)} + \frac{19 \log{\left(x \right)}}{3}\right) - 1 = 2 \log{\left(x \right)} + 1$$
$$\frac{22 \log{\left(x \right)}}{3} = 2$$
Let's divide both parts of the equation by the multiplier of log =22/3
$$\log{\left(x \right)} = \frac{3}{11}$$
This equation is of the form:
By definition log
then
$$x = e^{\frac{2}{\frac{22}{3}}}$$
simplify
$$x = e^{\frac{3}{11}}$$
$$\left(3 \log{\left(x \right)} + \frac{19 \log{\left(x \right)}}{3}\right) - 1 = 2 \log{\left(x \right)} + 1$$
$$\frac{22 \log{\left(x \right)}}{3} = 2$$
Let's divide both parts of the equation by the multiplier of log =22/3
$$\log{\left(x \right)} = \frac{3}{11}$$
This equation is of the form:
log(v)=p
By definition log
v=e^p
then
$$x = e^{\frac{2}{\frac{22}{3}}}$$
simplify
$$x = e^{\frac{3}{11}}$$
Sum and product of roots
[src]
sum
3/11 e
$$e^{\frac{3}{11}}$$
=
3/11 e
$$e^{\frac{3}{11}}$$
product
3/11 e
$$e^{\frac{3}{11}}$$
=
3/11 e
$$e^{\frac{3}{11}}$$
exp(3/11)