Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 15*x^2-4*x-3=0
- Equation 64-x^2=0
-
Equation 9^x=27
-
Equation 4^x-3*2^x=40
- Express {x} in terms of y where:
- 7*x-7*y=-8
- 15*x+8*y=13
- 20*x-15*y=19
- 8*x-7*y=-1
- Derivative of:
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9^x
- Integral of d{x}:
-
9^x
- Limit of the function:
-
9^x
- Sum of series:
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27
-
Identical expressions
- nine ^x= twenty-seven
- 9 to the power of x equally 27
- nine to the power of x equally twenty minus seven
- 9x=27
9^x=27 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$9^{x} = 27$$
or
$$9^{x} - 27 = 0$$
or
$$9^{x} = 27$$
or
$$9^{x} = 27$$
- this is the simplest exponential equation
Do replacement
$$v = 9^{x}$$
we get
$$v - 27 = 0$$
or
$$v - 27 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 27$$
We get the answer: v = 27
do backward replacement
$$9^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(9 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(27 \right)}}{\log{\left(9 \right)}} = \frac{3}{2}$$
$$9^{x} = 27$$
or
$$9^{x} - 27 = 0$$
or
$$9^{x} = 27$$
or
$$9^{x} = 27$$
- this is the simplest exponential equation
Do replacement
$$v = 9^{x}$$
we get
$$v - 27 = 0$$
or
$$v - 27 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 27$$
We get the answer: v = 27
do backward replacement
$$9^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(9 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(27 \right)}}{\log{\left(9 \right)}} = \frac{3}{2}$$
Rapid solution
[src]
x1 = 3/2
$$x_{1} = \frac{3}{2}$$
log(27) pi*I
x2 = -------- + ------
2*log(3) log(3)
$$x_{2} = \frac{\log{\left(27 \right)}}{2 \log{\left(3 \right)}} + \frac{i \pi}{\log{\left(3 \right)}}$$
x2 = log(27)/(2*log(3)) + i*pi/log(3)
Sum and product of roots
[src]
sum
3 log(27) pi*I - + -------- + ------ 2 2*log(3) log(3)
$$\frac{3}{2} + \left(\frac{\log{\left(27 \right)}}{2 \log{\left(3 \right)}} + \frac{i \pi}{\log{\left(3 \right)}}\right)$$
=
3 log(27) pi*I - + -------- + ------ 2 2*log(3) log(3)
$$\frac{3}{2} + \frac{\log{\left(27 \right)}}{2 \log{\left(3 \right)}} + \frac{i \pi}{\log{\left(3 \right)}}$$
product
/log(27) pi*I \
3*|-------- + ------|
\2*log(3) log(3)/
---------------------
2
$$\frac{3 \left(\frac{\log{\left(27 \right)}}{2 \log{\left(3 \right)}} + \frac{i \pi}{\log{\left(3 \right)}}\right)}{2}$$
=
9 3*pi*I - + -------- 4 2*log(3)
$$\frac{9}{4} + \frac{3 i \pi}{2 \log{\left(3 \right)}}$$
9/4 + 3*pi*i/(2*log(3))
The graph