Solve the quadratic equation 5^2x- 5^{x + 3}+ 125 = 5^x.

Solve \(\sqrt [ 8 ]{{{x}\over{x+3}} } -\sqrt{{{x+3}\over{x}}}=2.\)

A factory kept increasing its out-put by the same percentage every year. Find the percentage, if it is known that the output has doubled in the last two years.

Find the value of log₂ \(\left({{\sqrt [ 3 ]{4 } }\over{4^2\sqrt{8}}} \right).\)

Find x if \({{1}\over{2}}\) log₁₀ \((11+4\sqrt{7})\) = log₁₀ (2 + x).

Solve 23x < 100 when
(i) x is a natural number
(ii) x is an integer.

Prove that \(log_{10}2+16log_{10}\frac { 16 }{ 15 } +12log_{10}\frac { 25 }{ 24 } +7log_{10}\frac { 81 }{ 80 } =1\)

A plumber can be paid according to the following schemes: In the first scheme he will be paid rupees 500 plus rupees 70 per hour, and in the second scheme he will be paid rupees 120 per hour. If he works x hours, then for what value of x does the first scheme give better wages?

Solve the equation \(\sqrt{6-4x-x^2}=x+4\)

Find a quadratic polynomial f(x) such that, f(0) = 1; f(-2) = 0 and f(1) = 0.