If (x+1)^log10_(x+1)=100(x+1),then x equals
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Answer:
Step-by-step explanation:
Making
y
=
x
−
1
we have
y
log
e
y
=
100
y
→
y
log
e
y
−
1
=
100
Applying
log
to both sides
(
log
e
y
−
1
)
log
e
y
=
log
e
100
Solving for
log
e
y
we have
log
e
y
=
1
2
(
1
±
√
1
+
4
log
e
(
100
)
)
so
Y
=
x
−
1
=
e
1
2
(
1
±
√
1
+
4
log
e
(
100
)
)
Finally considering that
x
−
1
>
0
x
=
1
+
e
1
2
(
1
+
√
1
+
4
log
e
(
100
)
)
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