`log_2(x - 1) = 5` Solve the equation accurate to three decimal places

Saturday, January 8, 2011

$\displaystyle{\log}_{{2}}{\left({x}-{1}\right)}={5}$

To solve, convert the equation to exponential form.

Take note that if a logarithmic equation is in the form

$\displaystyle{y}={\log}_{{b}}{\left({x}\right)}$

its equivalent exponential equation is

$\displaystyle{x}={{b}}^{{y}}$

So converting

$\displaystyle{\log}_{{2}}{\left({x}-{1}\right)}={5}$

to exponential equation, it becomes

$\displaystyle{x}-{1}={{2}}^{{5}}$

Then, simplify the right side.

$\displaystyle{x}-{1}={32}$

And isolate the x.

$\displaystyle{x}={32}+{1}$

$\displaystyle{x}={33}$

Therefore, the solution is $\displaystyle{x}={33}$ .

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