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Evaluate the logarithmic expression Log subscript5^25 +log subscript 5^625/logsubscript5^100. The value of the expression, rounded to the nearest hundredth, is____.
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Evaluate the logarithmic expression Log subscript5^25 +log subscript 5^625/logsubscript5^100. The value of the expression, rounded to the nearest hundredth, is____.
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Apr 20, 2019
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Evaluate the logarithmic expression Log subscript5^25 +log subscript 5^625/logsubscript5^100. The value of the expression, rounded to the nearest hundredth, is____.
Mathematics
high-school
Sadeq Shahmoradi
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Hello !
Here are some rules for logarithms :
log ₐ b = n ⇔ aⁿ = b
log ₐ aⁿ = n
log ₐ (b·c) = log
ₐ b + log
ₐ c
log
ₐ bⁿ = n· log
ₐ b
____________________________________________________
25=5²
625=5⁴
100 = 5² · 2²
____________________________________________________
(log₅ 25 + log₅ 625) / log₅100 =
(log₅ 5²+ log₅ 5⁴) / log₅ (5² · 2²) =
(log₅ 5²+ log₅ 5⁴) /( log₅ 5² + log₅ 2²) =
(2 + 4)/(2+log₅ 2² ) =
6/ (2+2·log₅2)=
6/2 + 6/ (2·log₅2) =
3+ 3/log₅2
log₅2 = 0.5
So
3+ 3/log₅2
= 3 + 3/0.5 =3 + 6 =
9
Answer : 9
Ahmad Shahwan
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Apr 26, 2019
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Ahmad Shahwan
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