Question

If (625)* = 15625, find x2 and x3​

Answer 1

${625}^{x} = 15625 \\ {(5)}^{4x} = 625 \times 25 \\ {5}^{4x} = {5}^{(4 + 2)} \\ {5}^{4x} = {5}^{6}$

Therefore,

$4x = 6 \\ x = \frac{3}{2}$
Now,
${x}^{2} = {( \frac{3}{2} )}^{2} = \frac{9}{4}$
and,
${( \frac{3}{2} )}^{3} = \frac{27}{8}$
Hence the values required are gained.