Question

if x=log2aa, y=log3a2a, z=log4a3a; probe that xyz+1=2yz​

Answer 1

photo bhejo........

.

..

Answer 2

ANSWER:-

you can convert everything to base of 10 using the log base conversion formula of:

Lb(x) = L(x)/L(b)

that means log of x to the base of b is equivalent to log of x to the base of 10 divided by log of b to the base of 10.

your original equations get converted as follows:

x = L2a(a) becomes x = L(a)/L(2a)

y = L3a(2a) becomes y = L(2a)/L(3a)

z = L4a(3a) becomes z = L(3a)/L(4a)

applying these equivalencies, you get:

2yz = 2*L(2a)/L(3a)*L(3a)/L4a) which becomes:

2yz = 2*L(2a)/L(4a).

since 2*L(2a) becomes L((2a)^2) which becomes L(4a^2), then:

2yz = 2*L(2a)/L(4a) bcomes:

2yz = L(4a^2)/L(4a)

xyz+1 = L(a)/L(2a)*L(2a)/L(3a)*L(3a)/L(4a)+1 which becomes:

xyz+1 = L(a)/L(4a)+1 which becomes:

xyz+1 = L(a)/L(4a)+L(4a)/L(4a) which becomes:

xyz+1 = (L(a)+L(4a))/L(4a)

since L(a)+L(4a) is equal to L(a*4a) which is equal to L(4a^2), then:

xyz+1 = (L(a)+L(4a))/L(4a) becomes:

xyz+1 = L(4a^2)/L(4a).

since 2yz = L(4a^2)/L(4a) and xyz+1 = L(4a^2)/L(4a), then:

2yz = xyz+1