Question

if log x:3=log y :4=log z:5 then zx is​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

The value is $xz=y^2$.

Step-by-step explanation:

Given : If log x:3=log y :4=log z:5

To find : The value of zx ?

Solution :

If a:b:c:d then $\frac{a}{b}=\frac{c}{d}$

If log x:3=log y :4 then,

$\frac{\log x}{3}=\frac{\log y}{4}$

$4\log x=3\log y$

$\log x^4=\log y^3$

$x^4=y^3$ ....(1)

If log x:3=log y :4 then,

$\frac{\log y}{4}=\frac{\log z}{5}$

$5\log y=4\log z$

$\log y^5=\log z^4$

$y^5=z^4$

$z^4=y^5$  ....(2)

The value of zx is given by using (1) and (2),

Multiply (1) and (2),

$x^4\times z^4=y^3\times y^5$

$(xz)^4=y^8$

$xz=y^2$

Therefore, the value is $xz=y^2$.

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