Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation x+y=15
-
Equation -(-y+4)+2*y+1=0
-
Equation 11-5(2x+1)=41-9x
- Equation 2*x^2+50=0
- Express {x} in terms of y where:
- -16*x-20*y=-13
- 4*x+5*y=7
- -5*x+7*y=-18
- -11*x-20*y=9
-
Identical expressions
- log5(3x- two)=log5* seven
- logarithm of 5(3x minus 2) equally logarithm of 5 multiply by 7
- logarithm of 5(3x minus two) equally logarithm of 5 multiply by seven
- log5(3x-2)=log57
- log53x-2=log57
-
Similar expressions
- (log(19)/log(2))+(log(3)/log(2))=(log(57)/log(2))
- log(5^(7-2x))/log(125)=5
- log5(3x+2)=log5*7
- log5(7x+3)=log5(2x-5)
log5(3x-2)=log5*7 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
log(3*x - 2) ------------ = log(5)*7 log(5)
$$\frac{\log{\left(3 x - 2 \right)}}{\log{\left(5 \right)}} = 7 \log{\left(5 \right)}$$
Detail solution
Given the equation
$$\frac{\log{\left(3 x - 2 \right)}}{\log{\left(5 \right)}} = 7 \log{\left(5 \right)}$$
$$\frac{\log{\left(3 x - 2 \right)}}{\log{\left(5 \right)}} = 7 \log{\left(5 \right)}$$
Let's divide both parts of the equation by the multiplier of log =1/log(5)
$$\log{\left(3 x - 2 \right)} = 7 \log{\left(5 \right)}^{2}$$
This equation is of the form:
By definition log
then
$$3 x - 2 = e^{\frac{7 \log{\left(5 \right)}}{\frac{1}{\log{\left(5 \right)}}}}$$
simplify
$$3 x - 2 = e^{7 \log{\left(5 \right)}^{2}}$$
$$3 x = 2 + e^{7 \log{\left(5 \right)}^{2}}$$
$$x = \frac{2}{3} + \frac{e^{7 \log{\left(5 \right)}^{2}}}{3}$$
$$\frac{\log{\left(3 x - 2 \right)}}{\log{\left(5 \right)}} = 7 \log{\left(5 \right)}$$
$$\frac{\log{\left(3 x - 2 \right)}}{\log{\left(5 \right)}} = 7 \log{\left(5 \right)}$$
Let's divide both parts of the equation by the multiplier of log =1/log(5)
$$\log{\left(3 x - 2 \right)} = 7 \log{\left(5 \right)}^{2}$$
This equation is of the form:
log(v)=p
By definition log
v=e^p
then
$$3 x - 2 = e^{\frac{7 \log{\left(5 \right)}}{\frac{1}{\log{\left(5 \right)}}}}$$
simplify
$$3 x - 2 = e^{7 \log{\left(5 \right)}^{2}}$$
$$3 x = 2 + e^{7 \log{\left(5 \right)}^{2}}$$
$$x = \frac{2}{3} + \frac{e^{7 \log{\left(5 \right)}^{2}}}{3}$$
Sum and product of roots
[src]
sum
2
7*log (5)
2 e
- + ----------
3 3
$$\frac{2}{3} + \frac{e^{7 \log{\left(5 \right)}^{2}}}{3}$$
=
2
7*log (5)
2 e
- + ----------
3 3
$$\frac{2}{3} + \frac{e^{7 \log{\left(5 \right)}^{2}}}{3}$$
product
2
7*log (5)
2 e
- + ----------
3 3
$$\frac{2}{3} + \frac{e^{7 \log{\left(5 \right)}^{2}}}{3}$$
=
2
7*log (5)
2 e
- + ----------
3 3
$$\frac{2}{3} + \frac{e^{7 \log{\left(5 \right)}^{2}}}{3}$$
2/3 + exp(7*log(5)^2)/3
Rapid solution
[src]
2
7*log (5)
2 e
x1 = - + ----------
3 3
$$x_{1} = \frac{2}{3} + \frac{e^{7 \log{\left(5 \right)}^{2}}}{3}$$
x1 = 2/3 + exp(7*log(5)^2)/3
Numerical answer
[src]
x1 = 24975864.4843036
x2 = 24975864.4843036 - 2.39932855713934e-19*i
x2 = 24975864.4843036 - 2.39932855713934e-19*i