Question

slm herkese ...


a=?

not report my questions for no reason​

Answer 1

Doğru cevap A seçeneğidir.

Üstel fonksiyonun temel özelliklerini zaten bildiğinizi varsayıyorum.

#Teşekkürler !

Answer 2

The right option is A .

Step-by-step explanation:

To Solve:

$\sqrt{2 \sqrt[3]{ \frac{1}{2} \sqrt[5]{ \frac{1}{4} } } } = {2}^{a}$

Solution:

Remember, This question is related to Laws of Indices.

So, 1st split the exponent in smaller form. i.e 27 = 3³ and 6² = 2². 3²

2nd Solve by using laws of Indices as required.

L.H.S

$\sqrt{2 \sqrt[3]{ \frac{1}{2} \sqrt[5]{ \frac{1}{4} } } } \\ \\ \sqrt{ 2\sqrt[3]{ { \frac{1}{2}. \sqrt[5]{ {( \frac{1}{2}) }^{2} } } }} \\ \\ \sqrt{ 2\sqrt[3]{ \frac{1}{2}. { \frac{1}{2} }^{ (\frac{2}{5})}}} \\ \\ \sqrt{2 {( \frac{1}{2} )}^{(1 + \frac{2}{5}) \frac{1}{3} } } \\ \\ \sqrt{2 {( \frac{1}{2} )}^{( \frac{5 + 2}{5}) \frac{1}{3} } } \\ \\ \sqrt{2 {( \frac{1}{2} )}^{(\frac{7}{15}) } } \\ \\ \sqrt{2. {2}^{ - 1( \frac{7}{15} )} } = 0 \\ \\ \sqrt{ {2}^{1 - \frac{7}{15} } } \\ \\ \sqrt{ {2}^{ \frac{8}{15} } } \\ \\ {2}^{ \frac{8}{15} \times \frac{1}{2} } \\ \\ {2}^{ \frac{4}{15} }$

Now, Comparing the L.H.S and R.H.S

${2}^{ \frac{4}{15} } = {2}^{a}\\\\ [\text{Eliminating the base from both side}] \\\\\frac{4}{15} = a$

The, required answer is a = 4/15.

${\boxed{\blue{\text{ Some Important Laws of Indices}}}}$

${a}^{n}.{a}^{m}={a}^{(n + m)}$

${a}^{-1}=\dfrac{1}{a}$

$\dfrac{{a}^{n}}{ {a}^{m}}={a}^{(n-m)}$

${({a}^{c})}^{b}={a}^{b\times c}={a}^{bc}$

${a}^{\frac{1}{x}}=\sqrt[x]{a}$

$[\text{where all variables are real and greater than 0}]$