What is (((ln(x)-ln(100)))/(sqrt(2*ln(2))))^2 ?

The solution to (((ln(x)-ln(100)))/(sqrt(2*ln(2))))^2 is (ln^2(x/(100)))/(2ln(2))

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simplify (((ln(x)-ln(100)))/(sqrt(2*ln(2))))^2

simplify

(\frac{( ln ( x ) - ln ( 100 ) )}{2 \cdot ln ( 2 )})^{2}

\frac{ln ^{2} ( \frac{x}{100} )}{2 ln ( 2 )}

Solution steps

(\frac{( ln ( x ) - ln ( 100 ) )}{2 ln ( 2 )})^{2}

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (x) - ln (100) = ln (\frac{x}{100})

= (\frac{ln ( \frac{x}{100} )}{2 ln ( 2 )})^{2}

\frac{ln ( \frac{x}{100} )}{2 ln ( 2 )} = \frac{ln ( \frac{x}{100} )}{2 ln ( 2 )}

= (\frac{ln ( \frac{x}{100} )}{2 ln ( 2 )})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{ln ^{2} ( \frac{x}{100} )}{( 2 ln ( 2 ) ) ^{2}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(2 ln (2))^{2} = (2)^{2} (ln (2))^{2}

= \frac{ln ^{2} ( \frac{x}{100} )}{( 2 ) ^{2} ( ln ( 2 ) ) ^{2}}

(2)^{2} : 2

= \frac{ln ^{2} ( \frac{x}{100} )}{2 ( ln ( 2 ) ) ^{2}}

(ln (2))^{2} : ln (2)

= \frac{ln ^{2} ( \frac{x}{100} )}{2 ln ( 2 )}

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100 + 20 \cdot ln (\frac{65}{65 - 30})

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What is (((ln(x)-ln(100)))/(sqrt(2*ln(2))))^2 ?
The solution to (((ln(x)-ln(100)))/(sqrt(2*ln(2))))^2 is (ln^2(x/(100)))/(2ln(2))