Question

Find the value of logy (x4 ) if logx (y3 ) = 2

Answer 1

Given:

logₓ (y³) = 2

To find:

The value of  logᵧ (x⁴)

Calculation:

We know the formula logₐ xⁿ = n(logₐ x). By substituting the formula in the given data

     $\Rightarrow log_x(y^3) =2\\ \\\Rightarrow 3log_x(y) =2 \\ \\\Rightarrow log_x(y) =\frac{2}{3}$

We know the formula logₐx = 1 / logₓa. By substituting the formula in thaw above equation, we get

     $\Rightarrow log_y(x) = \frac{3}{2} \\ \\\Rightarrow 4 log_y(x) =4\times \frac{3}{2} \\ \\\Rightarrow log_y(x^4) = 6$

Final answer:

The value of logᵧ (x⁴) is 6