Question

If x = 1 + log 2 - log 5, y = 2 log 3 and
z = log a - log 5; find the value of a, if
x+y= 2z​

Answer 1

Answer:

a = 10

Step-by-step explanation:

x + y = 2z

1+log2-log5 = 2(log a - log 5)

log10+log2-log5 =2loga-2log5

log(2*5)+log2-log5=loga^2-log 5^2

=log2+log5+log2-log5=loga^2-log25

2log2 = log(a^2/25)

log2^2= log(a^2/25)

log4 =log(a^2/25)

4 = a^2/25

a^2 = 25*4=100

a=10

Note :

1) 1 = log 10

2) m log a = log a^m

3) log a - log b = log a/b