Question

if 5^a=7^b=35^c,then c=?

1)a-b/ab
2)ab/a-b
3)a+b/ab
4)ab/a+b​

Answer 1

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Answer 2

The value of c is ab/(a + b) , hence the correct option is (4) ab/(a + b).

$5^a=7^b=35^c$

We have to find the value of c.

$5^a=7^b=35^c=k(\text{Let})$

$\implies 5=k^{1/a}$

$\implies 7^b=k^{1/b}$

$\implies 35^c=k^{1/c}$

we know, 35 = 5 × 7

$\implies k^{1/c}=k^{1/a}\times k^{1/b}$

we know,

$x^m\times x^n=x^{m+n}$

$\implies k^{1/c}=k^{\left(\frac{1}{a}+\frac{1}{b}\right)}$

we also know,

$x^m=x^n\implies m=n$

$\implies\frac{1}{c}=\frac{1}{a}+\frac{1}{b}=\frac{a+b}{ab}$

$\implies c=\frac{ab}{a+b}$

Therefore the value of c is ab/(a + b).