Question

4. In each of the following assumethat the base is 10. Prove that: . (i) log (1) + log(?) + log(?) + log(;) - log(})=0. (ii) log360 = 3log2 + 2log3 + log5 (iii)log (29) = log2 + 2log5 - log3 – 2log7. 50 147 (iv) log(10) + log(100) + log(1000) + log(10000) = 10. (v) 5log3 - log9 = log27. ​

Answer 1

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• log(10) + log(100) + log(1000) + log(10000) = 10.

definition of logarithm

• y = log x (base 10 is implied)
• 10^y = x

therefore

• 10^1 = 10
• 10^2 = 100
• 10^3 = 1000
• 10^4 = 10000

• log(10) + log(100) + log(1000) + log(10000) = 1 + 2 + 3 + 4 = 10

Answer 2

Answer:

each of the following assumethat the base is 10. Prove that: . (i) log (1) + log(?) + log(?) + log(;) - log(})=0. (ii) log360 = 3log2 + 2log3 + log5 (iii)log (29) = log2 + 2log5 - log3 – 2log7. 50 147 (iv) log(10) + log(100) + log(1000) + log(10000) = 10. (v) 5log3 - log9 = log27.

Step-by-step explanation:

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