Log√27-log√28/log3-log2
Answers
Explanation:
Step: 1
The radicand of each logarithmic term in the numerator can be converted as cube of a number.
=
log
√
3
3
+
log
√
2
3
−
log
√
5
3
log
6
−
log
5
Step: 2
The symbol square root (
√
) represents an exponent
1
2
.
=
log
(
3
3
)
1
2
+
log
(
2
3
)
1
2
−
log
(
5
3
)
1
2
log
6
−
log
5
Use power rule of exponents to simplify power of an exponential term.
=
log
(
3
)
3
2
+
log
(
2
)
3
2
−
log
(
5
)
3
2
log
6
−
log
5
Step: 3
The number of the logarithm term is in exponential notation. So, apply power rule of the logarithms to simplify each term in the numerator.
=
3
2
(
log
3
)
+
3
2
(
log
2
)
−
3
2
(
log
5
)
log
6
−
log
5
Step: 4
The rational number
3
2
is a common multiplying factor of each logarithmic term in numerator. So, take
3
2
common from three terms.
=
3
2
[
log
3
+
log
2
−
log
5
]
log
6
−
log
5
Step: 5
It can be expressed as two multiplying factors.
=
3
2
×
log
3
+
log
2
−
log
5
log
6
−
log
5
Step: 6
Observe the expression in numerator and denominator carefully. The numerator can be expressed same as the expression in the denominator by applying product rule of logarithms to addition of
log
3
and
log
2
terms.
=
3
2
×
log
(
3
×
2
)
−
log
5
log
6
−
log
5
=
3
2
×
log
6
−
log
5
log
6
−
log
5
=
3
2
×
log
6
−
log
5
log
6
−
log
5
=
3
2
×
1
∴
log
√
27
+
log
√
8
−
log
√
125
log
6
−
log
5
=
3
2
Therefore, the answer for this problem is
3
2
and it is required solution for this logarithm problem mathematically.