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WAEC Mathematics 2023 Paper
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© africaexams.com
Question : 15
Total: 50
If
log
a
3
\log_a 3
lo
g
a
3
= m and
log
a
5
\log_a 5
lo
g
a
5
= p, find
log
a
75
\log_a 75
lo
g
a
75
m
2
+
p
m^2 + p
m
2
+
p
2m + p
m + 2p
m
+
p
2
m + p^2
m
+
p
2
Validate
Solution:
Given:
log
a
3
\log_a 3
lo
g
a
3
= m and
log
a
5
\log_a 5
lo
g
a
5
= p
log
a
75
\log_a 75
lo
g
a
75
=
log
a
(
3
×
25
)
\log_a (3 \times 25)
lo
g
a
(
3
×
25
)
=
log
a
(
3
×
5
2
)
\log_a (3 \times 5^2)
lo
g
a
(
3
×
5
2
)
=
log
a
3
+
log
a
5
2
\log_a 3 + \log_a 5^2
lo
g
a
3
+
lo
g
a
5
2
=
log
a
3
+
2
log
a
5
\log_a 3 + 2\log_a 5
lo
g
a
3
+
2
lo
g
a
5
Since
log
a
3
\log_a 3
lo
g
a
3
= m and
log
a
5
\log_a 5
lo
g
a
5
= p
∴
log
a
75
\log_a 75
lo
g
a
75
= m + 2p
© africaexams.com
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