Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 2^x=6-x
-
Equation x+12=5
-
Equation x^3=4
-
Equation x^2+2x+2=0
- Express {x} in terms of y where:
- 15*x-5*y=-5
- 18*x+20*y=-2
- -5*x-6*y=-1
- -17*x-15*y=-17
- Derivative of:
-
5^x
- Integral of d{x}:
-
5^x
- Graphing y =:
-
5^x
- Sum of series:
-
125
-
Identical expressions
- five ^x= one hundred and twenty-five
- 5 to the power of x equally 125
- five to the power of x equally one hundred and twenty minus five
- 5x=125
-
Similar expressions
- 20*5^(2*x)-12*5^x+1=0
- (25^(x-1,5))-(12*5^(x-2))+7=0
5^x=125 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$5^{x} = 125$$
or
$$5^{x} - 125 = 0$$
or
$$5^{x} = 125$$
or
$$5^{x} = 125$$
- this is the simplest exponential equation
Do replacement
$$v = 5^{x}$$
we get
$$v - 125 = 0$$
or
$$v - 125 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 125$$
We get the answer: v = 125
do backward replacement
$$5^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(5 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(125 \right)}}{\log{\left(5 \right)}} = 3$$
$$5^{x} = 125$$
or
$$5^{x} - 125 = 0$$
or
$$5^{x} = 125$$
or
$$5^{x} = 125$$
- this is the simplest exponential equation
Do replacement
$$v = 5^{x}$$
we get
$$v - 125 = 0$$
or
$$v - 125 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 125$$
We get the answer: v = 125
do backward replacement
$$5^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(5 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(125 \right)}}{\log{\left(5 \right)}} = 3$$
The graph