Expressing x in Terms of y, to Find the Range of a Function

Q.

Find the value of x if $(2x{)}^{ln2}$ = $(3y{)}^{ln3}$ and $3^{lnx}$ = $2^{lny}$.

${\log }_{e}x$ can also be written as ln(x)

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Q.

If $S_1,S_2,S_3--------S_n$ denotes the sum of 1, 2, 3 ----n terms of an A.P, having first term a. If $\frac{Skx}{Sx}$ k $\ne$ 1, is independent of x, then $S_1+S_2+S_3--------S_n$ =

1. 

2. 

3. 

4. 

Q. Range of f(x) = x² is

f(x) = x² का परिसर है

1. R
2. (3, ∞)
3. (2, ∞)
4. [0, ∞)