# 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

Answer

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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.

Last updated date: 20th Sep 2023

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