Question

if 3^x=5^y =15^z then, 1/z =1/x+1/y

Answer 1

SOLUTION

GIVEN

$\displaystyle \sf{ {3}^{x} = {5}^{y} = {15}^{z} }$

TO PROVE

$\displaystyle \sf{ \frac{1}{z} = \frac{1}{x} + \frac{1}{y} }$

EVALUATION

Here it is given that

$\displaystyle \sf{ {3}^{x} = {5}^{y} = {15}^{z} = k \: (say) }$

Thus we get

$\displaystyle \sf{ 3 = {k}^{ \frac{1}{x} } }$

$\displaystyle \sf{ 5 = {k}^{ \frac{1}{y} } }$

$\displaystyle \sf{ 15 = {k}^{ \frac{1}{z} } }$

Now

3 × 5 = 15

$\displaystyle \sf{ \implies \: {k}^{ \frac{1}{x} }. {k}^{ \frac{1}{y} } = {k}^{ \frac{1}{z} }}$

$\displaystyle \sf{ \implies \: {k}^{ \frac{1}{x} + \frac{1}{y} }= {k}^{ \frac{1}{z} }}$

$\displaystyle \sf{ \implies \: \frac{1}{x} + \frac{1}{y} = \frac{1}{z} }$

Hence proved

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. If x/5 = y/3 then 3x + 5y / … fill in the blanks by choosing correct answer

https://brainly.in/question/39275501

2. if 7m + 4n = 3m + 2n then m/n = ?

https://brainly.in/question/39272649