Question

If x= log 0.6, y=log 1.25 and z= log3- 2log2
find the value of x+y-z

Answer 1

check the attachment

Answer 2

The value is x+y-z=0.

Step-by-step explanation:

Given : $x= \log 0.6,\ y=\log 1.25 \text{ and } z= \log3- 2\log2$

To find : The value of x+y-z ?

Solution :

Using logarithmic identity,

$\log a-\log b=\log (\frac{a}{b})$

$\log a+\log b=\log (ab)$

$a\log x=\log x^a$

Re-write z as

$z=\log 3-\log 2^2$

$z=\log \frac{3}{4}$

$z=\log 0.75$

Now substitute the values,

$x+y-z=\log 0.6+\log 1.25-\log 0.75$

$x+y-z=\log \frac{(0.6\times 1.25)}{0.75}$

$x+y-z=\log 1$

$x+y-z=0$

Therefore, the value is x+y-z=0.

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