Question

if $if 4^{x} = 5^{y} = 20^{z} then the value of z is$

Answer 1

4^x = 5^y = 20^z = K

4^x = K
take log both sides
xlog4 = logK
log4 = logK/ x ------(1)

similarly,
5^y = K
log5 = logK/y ------------(2)

and ,
20^z = K
z = logK/log20
= logK/log(5×4)
= logK/{ log5 + log4}

put eqns (1) and (2)

z = logK/{ logK/x + logK/y}

= 1/( 1/x + 1/y )

= xy/( x + y)

hence, z = xy/( x + y)

Answer 2

Answer:

brainliest

Step-by-step explanation:

4xy5xy=20zy20zx  

20xy=20zy+zx

xy=zy+zx

z=11x+1y

Note that this is only true, when 4x=5y and unfortunately gcd(4,5)=1, so the only valid value for z is 0.

The expression would be far more interesting, if your equations were:

ax=by=(ab)z where gcd(a,b)=min(a,b)

For example, if the equation was:

2x=4y=8z

Then, x = 4 and y = 2, satisfy the condition 2x=4y, so from above, z = 4/3 and we know that 84/3=16.