Question

If log x/2=log y/3 = log z/5, then yz in terms of x is

Answer 1

y = x^(3/2) and z = x^(5/2)

Given,

 $\frac{logx}{2} =\frac{logy}{3} =\frac{logz}{5}$

To Find,

y and z in terms of x

Solution,

$\frac{logx}{2} =\frac{logy}{3}$        (Given)

$= > log x = \frac{2}{3} log y$

Using the power rule of the logarithm,

we get,

$log x = log y^{2/3}$

Taking anti-log on both sides,

$x=y^{2/3} \\= > y = x^{3/2}$

Similarly,

$\frac{logx}{2} =\frac{logz}{5}$        (Given)

$= > log x = \frac{2}{5} log z$

Using the power rule of the logarithm,

we get,

$log x = log z^{2/5}$

Taking anti-log on both sides,

$x=z^{2/5} \\= > z = x^{5/2}$

Therefore,  y = x^(3/2) and z = x^(5/2)

Answer 2

The value of yz in terms of x is yz = x⁴.

Given,

The value of log x/2=log y/3 = log z/5.

To Find,

The value of yz in terms of x.

Solution,

The given expression is

log x/2=log y/3 = log z/5

So,

log x/2=log y/3

log x = 2/3 log y

Now, using the property of logarithm

n log m = log mⁿ

$log x = logy^{2/3}$

$y = x^{3/2}$---(i)

Now,

log x/2 = log z/5

log z = 5/2 log x

$z = x^{5/2}$---(ii)

Multiply (i) and (ii)

$yz = x^{3/2+5/2}$

yz = x⁴

Hence, the value of yz in terms of x is yz = x⁴.

#SPJ3