Question

help me plzzz and give its correct answer plzz.​

Answer 1

Step-by-step explanation:

u just need to understand the geometric progressions

Answer 2

✰Answer✰

☛Given:

$\large{ \sf{ \bullet{ \: \: \: {2}^{a} = {5}^{b} = {10}^{c} }}}$

☛To prove:

$\large{ \sf{ \bullet{ \: \: \: \frac{1}{a} + \frac{1}{b} = \frac{1}{c} }}}$

✰Proof✰

$\red{ \tt{Let \: {2}^{a} = {5}^{b} = {10}^{c} = k }}$

☛Now let see individually,

$\large{ \sf{ \rightarrow \: {2}^{a} = k}} \\ \\ \large{ \sf{ \rightarrow \: 2 = {k}^{ \frac{1}{a}} .........(1)}}$

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$\large{ \sf{ \rightarrow \: {5}^{b} = k}} \\ \\ \large{ \sf{ \rightarrow \: 5 = {k}^{ \frac{1}{b} } .......(2)}}$

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$\large{ \sf{ \rightarrow \: {10}^{c} = k}} \\ \\ \large{ \sf{ \rightarrow \: 10 = {k}^{ \frac{1}{c} }.......(3) }}$

━━━━━━━━━━━━

☛Now multiplying Equation 1 and 2 ,

$\rightarrow \tt{2 \times 5 = 10 }$

$\rightarrow \tt{{(K)}^{ \frac{1}{a}} + {(K)}^{ \frac{1}{b}} = {(K)}^{ \frac{1}{c}}}$

$\green{\tt{\underline{\underline{from \: equatin(3)}}}}$

$\rightarrow \tt{{(K)}^{ \frac{1}{a} + \frac{1}{b}} = {(K)}^{ \frac{1}{c}}}$

$\green{\tt{\underline{\underline{by \:\:using \:\: ({a}^{x}\times {a}^{y}={a}^{x+y})}}}}$

$\rightarrow \red{\boxed{\tt{ \frac{1}{a} + \frac{1}{b}=\frac{1}{c} }}}$

$\therefore \tt{hence\: proved}$