Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x+10)^2=(2-x)^2
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Equation -7-x=3x+17
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Equation -9а+8=-10а-2
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Equation (x+10)2=(5-x)2
- Express {x} in terms of y where:
- -9*x+12*y=-6
- -9*x-2*y=-15
- -1*x-5*y=3
- -7*x+6*y=12
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Identical expressions
- log(y+ one)=Const-log(cos(x))
- logarithm of (y plus 1) equally Const minus logarithm of ( co sinus of e of (x))
- logarithm of (y plus one) equally Const minus logarithm of ( co sinus of e of (x))
- logy+1=Const-logcosx
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Similar expressions
- log(y-1)=Const-log(cos(x))
- log(y+1)=Const+log(cos(x))
- log(y)+1/y=1/x+log(x)
- (log(y)+1)/y=c-log(x)
- log(y+1)=Const-log(cosx)
log(y+1)=Const-log(cos(x)) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
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log(y + 1) = c - log(cos(x))
$$\log{\left(y + 1 \right)} = c - \log{\left(\cos{\left(x \right)} \right)}$$
The graph
Rapid solution
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/ / c \\ / / c \\
| | e || | | e ||
x1 = - re|acos|-----|| + 2*pi - I*im|acos|-----||
\ \1 + y// \ \1 + y//
$$x_{1} = - \operatorname{re}{\left(\operatorname{acos}{\left(\frac{e^{c}}{y + 1} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{e^{c}}{y + 1} \right)}\right)} + 2 \pi$$
/ / c \\ / / c \\
| | e || | | e ||
x2 = I*im|acos|-----|| + re|acos|-----||
\ \1 + y// \ \1 + y//
$$x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(\frac{e^{c}}{y + 1} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{e^{c}}{y + 1} \right)}\right)}$$
x2 = re(acos(exp(c)/(y + 1))) + i*im(acos(exp(c)/(y + 1)))
Sum and product of roots
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sum
/ / c \\ / / c \\ / / c \\ / / c \\
| | e || | | e || | | e || | | e ||
- re|acos|-----|| + 2*pi - I*im|acos|-----|| + I*im|acos|-----|| + re|acos|-----||
\ \1 + y// \ \1 + y// \ \1 + y// \ \1 + y//
$$\left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{e^{c}}{y + 1} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{e^{c}}{y + 1} \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{acos}{\left(\frac{e^{c}}{y + 1} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{e^{c}}{y + 1} \right)}\right)} + 2 \pi\right)$$
=
2*pi
$$2 \pi$$
product
/ / / c \\ / / c \\\ / / / c \\ / / c \\\ | | | e || | | e ||| | | | e || | | e ||| |- re|acos|-----|| + 2*pi - I*im|acos|-----|||*|I*im|acos|-----|| + re|acos|-----||| \ \ \1 + y// \ \1 + y/// \ \ \1 + y// \ \1 + y///
$$\left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{e^{c}}{y + 1} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{e^{c}}{y + 1} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{acos}{\left(\frac{e^{c}}{y + 1} \right)}\right)} - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{e^{c}}{y + 1} \right)}\right)} + 2 \pi\right)$$
=
/ / / c \\ / / c \\\ / / / c \\ / / c \\\ | | | e || | | e ||| | | | e || | | e ||| -|I*im|acos|-----|| + re|acos|-----|||*|-2*pi + I*im|acos|-----|| + re|acos|-----||| \ \ \1 + y// \ \1 + y/// \ \ \1 + y// \ \1 + y///
$$- \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{e^{c}}{y + 1} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{e^{c}}{y + 1} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{e^{c}}{y + 1} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{e^{c}}{y + 1} \right)}\right)} - 2 \pi\right)$$
-(i*im(acos(exp(c)/(1 + y))) + re(acos(exp(c)/(1 + y))))*(-2*pi + i*im(acos(exp(c)/(1 + y))) + re(acos(exp(c)/(1 + y))))