(1) Write five laws of exponents with example.
Answers
Answer:
is this ok
Step-by-step explanation:
As the name of an exponential function is defined, it involves an exponent. This exponent is represented using a variable rather than a constant. On the other hand, its base is represented with constant value rather than a variable.
Let
f
(
x
)
=
a
b
x
This is an exponential function where “b” is a constant, the exponent “x” is the independent variable i.e. input of the function. The coefficient “a” is called the initial value of the function, f(x) represents the dependent variable i.e. output of the function. Thus for x > 1, the value of f(x) will always increase for increasing values of x.
The exponential property can be used to solve the equations with exponential functions. Exponential functions defined by an equation of the form as above are called exponential decay functions if the change factor b follows the inequality 0 < b < 1.
The good thing about exponential functions is that they are very useful in real-world situations. Exponential functions are used to model the growth of populations, carbon date artifacts, help coroners to determine the time of death, compute the investments and compound interest, decay rate of radioactive elements as well as many other applications.
Exponentiation Formula
Quick summary
with stories
Characteristic and Mantissa of a Number
2 mins read
use of log tables to find logarithm of a number
3 mins read
Some Basic Exponential Formula:
In mathematics many useful formulas are available for exponential functions. We can directly use these in various equations to get values of unknown variables. Some of these formulas are given bellow:
Here we have assumed that x and y are variables and a, b, m, n are constants.
(1)
x
a
×
x
b
=
x
a
+
b
this is adding the exponets.
(2)
x
a
x
b
=
x
a
−
b
this is subtracting the exponents.
(3)
(
x
a
)
b
)
=
(
(
x
a
)
b
)
this is getting exponents of exponents.
(4)
(
x
y
)
a
=
x
a
×
y
a
this is expanding exponents of products.
(5)
x
0
=
1
this is giving value for zero exponent.
(6)
x
1
=
x
this is giving value for unit exponent.
(7)
(
x
−
(
n
)
=
1
x
n
this is giving value of negative exponent.
(8)
x
m
n
=
n
√
x
m
this is giving value of fractional exponent.
Solved Examples
Q.1: Find value of x ,
4
4
x
−
5
=
16
2
Solution:
Given:
4
4
x
−
5
=
16
2
We can express 16 as a power of 4,
i.e.
4
4
x
−
5
=
4
2
2
i.e.
4
4
x
−
5
=
4
4
Now comparing both sides of the above equation.
4x-5 = 4
4x = 4+5
4x = 9
x =
9
4
Q.2: Given the function f(x)=4^x , then evaluate each of the following.
(i) f(-2)
(ii) f(1)
(iii) f(0)
Solution:
(i)
f
(
x
)
=
4
x
So, put x=-2 we get
f
(
−
2
)
=
4
−
2
i.e.
f
(
−
2
)
=
1
4
2
i.e.
f
(
−
2
)
=
1
16
(ii)
f
(
x
)
=
4
x
Put x = 1
f
(
1
)
=
4
1
i.e.
f
(
1
)
=
4
(iii)
f
(
x
)
=
4
x
put x=0
we get
f
(
0
)
=
4
0
i.e. f(0) = 1
Revise
with Concepts
Reading Logarithmic Table
EXAMPLE
DEFINITIONS
FORMULAS
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Answer:
Step-by-step explanation:
