Question

if log x+1 base 2 is equal to 10 then x =​

Answer 1

$\large\underline{\sf{Given- }}$

$\rm :\longmapsto\: log_{2}(x + 1) = 10$

$\large\underline{\sf{To\:Find - }}$

$\rm :\longmapsto\:x$

$\large\underline{\sf{Solution-}}$

We know that

$\purple{\boxed{ \bf{ \: log_{x}(y) = z \: \implies \: y = {x}^{z}}}}$

Now,

Given that

$\rm :\longmapsto\: log_{2}(x + 1) = 10$

$\rm :\longmapsto\:x + 1 = {2}^{10}$

$\rm :\longmapsto\:x + 1 = 1024$

$\rm :\longmapsto\:x = 1024 - 1$

$\bf :\longmapsto\:x = 1023$

Additional Information :-

$\rm :\longmapsto\: log(xy) = log(x) + log(y)$

$\rm :\longmapsto\: log( {x}^{y} ) = y \: log(x)$

$\rm :\longmapsto\: log\dfrac{x}{y} = logx \: - \: logy$

$\rm :\longmapsto\: log_{x}(x) = 1$

$\rm :\longmapsto\: log_{x}(y) = \dfrac{logy}{logx}$

$\rm :\longmapsto\: {e}^{log \: x} = x$

$\rm :\longmapsto\: {e}^{y \: log \: x} = {x}^{y}$

$\rm :\longmapsto\: {a}^{ log_{a}(x)} = x$

$\rm :\longmapsto\: {a}^{ y \: log_{a}(x)} = {x}^{y}$