Question

If 10^x=196; find 10^((x/2)+1)

Answer 1

${10}^{x} = 196$

$\implies log_{10}196 = x$$\implies \: 2 \: log_{10}14 = x$

$\implies log_{10}14 = \frac{x}{2}$

Adding 1 to both the sides, we get,

$log_{10}(14) \: + 1 = \frac{x}{2} + 1$

$\implies log_{10} 14 + log_{10} 10 = \frac{x}{2} + 1$

$\implies log_{10}(14 \times 10) = \frac{x}{2} + 1$

$\implies log_{10} 140 = \frac{x}{2} + 1$

$\implies {10}^{ \frac{x}{2} + 1 } = 140$