Math, asked by deepa80, 2 months ago

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

Answers

Answered by mathdude500
2

\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}

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