If x = log 0.6, y = log 1.25 and z = log 3 – 2 log 2, then find the value of x + y – z.
A.0
B.1
C.2
D.3
Last updated date: 24th Mar 2023
•
Total views: 307.5k
•
Views today: 5.86k
Answer
307.5k+ views
Hint: We need to know the basic logarithmic formulae to solve the given problem.
Use product and division rule to solve the given problem.
Given x = log 0.6
y = log 1.25
z = log 3 – 2 log 2
x + y – z = log 0.6 + log 1.25 – (log 3 – 2 log 2)
$\left[ {\because \log A + \log B = \log (A \times B)\;\& \;\log A - \log B = \log \dfrac{A}{B}} \right]$
x + y – z = log (0.6$ \times $1.25) – log$\left( {\dfrac{3}{4}} \right)$
x + y – z = log 0.75 – log 0.75 = 0
$\therefore $ The value of x + y – z = 0
Note:
Logarithm is a way of showing how big a number is in terms of how many times you have to multiply a certain number (the base) to get it. It is the inverse function of exponentiation.
$ \Rightarrow y = {\log _e}x$ the inverse of this function will be $y = {e^x}$. We used product rule $\log A + \log B = \log (A \times B)$ and division rule $\log A - \log B = \log \dfrac{A}{B}$ in the above problem.
Use product and division rule to solve the given problem.
Given x = log 0.6
y = log 1.25
z = log 3 – 2 log 2
x + y – z = log 0.6 + log 1.25 – (log 3 – 2 log 2)
$\left[ {\because \log A + \log B = \log (A \times B)\;\& \;\log A - \log B = \log \dfrac{A}{B}} \right]$
x + y – z = log (0.6$ \times $1.25) – log$\left( {\dfrac{3}{4}} \right)$
x + y – z = log 0.75 – log 0.75 = 0
$\therefore $ The value of x + y – z = 0
Note:
Logarithm is a way of showing how big a number is in terms of how many times you have to multiply a certain number (the base) to get it. It is the inverse function of exponentiation.
$ \Rightarrow y = {\log _e}x$ the inverse of this function will be $y = {e^x}$. We used product rule $\log A + \log B = \log (A \times B)$ and division rule $\log A - \log B = \log \dfrac{A}{B}$ in the above problem.
Recently Updated Pages
If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts
What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?
