Question

if x=1+log2-log5, y=2log3 and z=loga-log5; find the value of a , if x+y=2z

Answer 1

If x=1+log2-log 5, & y=2log3 & also log a -log 5

With the help of given equatio x+y= 2Z WE can easily find the value of a

1+log2-log5+2log3 = 2log a- log 5

By log base a x power m= m log base a x

So. Log 2 -log 5 +log3^2=2(loga-log5)

By  loga-logb= loga/b

So log 2/5+ log9 =log(a/5)^2

= by loga+logb= loga×b

So log 2/5×9=loga^2/5^2

log18/5=loga^2/25

Now cancel log from both side

18/5=a^2/25

18×25/5=a^2

90=a^2

Under root of 90=a

a=30

HOPE THIS HELPS YOU

THANK YOU

Answer 2

HEY Buddy.....!! here is ur answer

Given that...... x = 1+log2-log5
y = 2log3
z = loga-log5

According to the question....

x+y = 2z

=> 1+log2-log5+2log3 = 2(loga–log5)

=> 1+log2-log5+2log5+2log3 = 2loga

=> 2loga = log10+log2+log5+log3²

[ log m×n = logm+logn, and log10 = 1]

=> 2loga = log(10×2×5×9)

=> 2loga = log(900)

=> loga² = log900

=> a² = 900

=> a = 30 <<<<< Ans.

I hope it will be helpful for you.....!!

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