Logarithms, Surds and Indices Test 2

Instructions

For the following questions answer them individually

Q 1

What is the value of x for which $$x^{2/3}$$ + $$3x^{1/3} - 4<0$$?

Q 2

$$\log_{2}X +\log_{4}X$$ = $$\log_{0.25}8$$. Solve for X

Q 3

What is the smallest integral value of ‘k’ for which $$8^k>10^6$$? (Assume that $$ \log_{10}{2}=0.301$$).

Q 4

If the square root of the number $$54+36\sqrt{2}$$ is represented in the form of $$a+b\sqrt{c}$$,where a, b, c are non-negative rational numbers, then find the minimum value of a+b+c

Q 5

Simplify: $$3 \log 6+ 10 \log 2 - 2 \log 12 - \log 3$$

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