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Mila [183]
3 years ago
9

URGENT HELP ME PLEASE

Mathematics
1 answer:
Trava [24]3 years ago
5 0

Answer:

(a)\log_3(\dfrac{81}{3})=3

(b)\log_5(\dfrac{625}{25})=2

(c)\log_2(\dfrac{64}{8})=3

(d)\log_4(\dfrac{64}{16})=1

(e)\log_6(36^4)=8

(f)\log(100^3)=6

Step-by-step explanation:

Let as consider the given equations are \log_3(\dfrac{81}{3})=?,\log_5(\dfrac{625}{25})=?,\log_2(\dfrac{64}{8})=?,\log_4(\dfrac{64}{16})=?,\log_6(36^4)=?,\log(100^3)=?.

(a)

\log_3(\dfrac{81}{3})=\log_3(27)

\log_3(\dfrac{81}{3})=\log_3(3^3)

\log_3(\dfrac{81}{3})=3        [\because \log_aa^x=x]

(b)

\log_5(\dfrac{625}{25})=\log_5(25)

\log_5(\dfrac{625}{25})=\log_5(5^2)

\log_5(\dfrac{625}{25})=2        [\because \log_aa^x=x]

(c)

\log_2(\dfrac{64}{8})=\log_2(8)

\log_2(\dfrac{64}{8})=\log_2(2^3)

\log_2(\dfrac{64}{8})=3        [\because \log_aa^x=x]

(d)

\log_4(\dfrac{64}{16})=\log_4(4)

\log_4(\dfrac{64}{16})=1        [\because \log_aa^x=x]

(e)

\log_6(36^4)=\log_6((6^2)^4)

\log_6(36^4)=\log_6(6^8)

\log_6(36^4)=8            [\because \log_aa^x=x]

(f)

\log(100^3)=\log((10^2)^3)

\log(100^3)=\log(10^6)

\log(100^3)=6            [\because \log10^x=x]

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