Logarithms, Surds and Indices Test 1

Instructions

For the following questions answer them individually

Q 1

If $$\log_{12}{81}=p$$, then $$3(\dfrac{4-p}{4+p})$$ is equal to

Q 2

If $$2^{m-1} + 2^{m+1} = 640$$, then what is the value of ‘m’?

Q 3

Find the sum of all the values of x which satisfy: $$log_x (5x - 6)$$ = $$x^{log_x 2}$$

Q 4

Evaluate the value of the expression.
$$\frac{1}{\sqrt4+\sqrt6}+\frac{1}{\sqrt6+\sqrt8}+\frac{1}{\sqrt8+\sqrt10}+....+\frac{1}{\sqrt98+\sqrt100}$$

Q 5

The two numbers $$4^{30}$$ and $$25^{30}$$ are written next to each other. What is the total number of digits written down?

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