Instructions

Answer the questions based on the following information. The following operations are defined for real numbers.

a # b=a + b, if a and b both are positive else a # b=1

a $$\triangledown$$ b=$$(a \times b)^{a+b}$$ if $$a\times\ b$$ is positive else a $$\triangledown$$b=1.

Question 48

$$\frac{((1\#1) \# 2) - (10^{1.3} \triangledown \log_{10}{0.1})}{1 \triangledown 2}$$

Solution

$$((1\#1) \# 2) = 2 \# 2 = 4$$

$$\log_{10} 0.1$$ = $$\log_{10} 10^{-1}$$ = -1

As $$(10^{1.3} \times -1)$$ is not positive, $$(10^{1.3} \triangledown \log_{10}{0.1})$$ = 1

$$1 \triangledown 2$$ = $$(1x2)^{(1+2)}$$ = $$2^3$$ = 8

Hence, the fraction is (4-1)/8 = 3/8


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