Question

if x,y,z are any three consecutive integers,find log (1+xy)​

Answer 1

Since x, y and z are consecutive integers.

Therefore,

• y = x+1
• z = x+2

Now,

$\quad \: \sf log_{10}(1 + xy)$

$= \sf log_{10}(1 + x(x + 1))$

$= \sf log_{10}(1 + {x}^{2} + x)$

$= \sf log_{10}(1) + log_{10}( {x}^{2} ) + log_{10}(x)$

$= \sf0 + 2 log_{10}(x) + log_{10}(x)$

$= \sf3 log_{10}(x)$