if log a[1+log b{1+log a x}]=0, then x =
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Step-by-step explanation:
We have,
log
a
(ab)=x
log
a
a+log
a
b=x [log
a
mn=log
a
m+log
a
n]
1+log
a
b=x [log
a
a=1]
log
a
b=x−1 ......(1)
Since,
=log
b
(ab)
=log
b
a+log
b
b
=log
b
a+1
=
log
a
b
1
+1 [
log
n
m
1
=log
m
n]
=
x−1
1
+1
=
x−1
1+x−1
=
x−1
x
Hence, this is the answer.
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