Question

How to solve this? ​

Answer 1

Answer of 17 is ㏒(
`x^(2)`+15x), Answer of 33 is x = 8 , Answer of 35 is x = ㏒10/㏒2 , Answer of 37 is x = -㏒12/㏒8 and Answer of 39 is x = 5

Explanation:

17. ㏒x + ㏒(x+15)

Using property ㏒a + ㏒b = ㏒a×b

∴ ㏒x + ㏒(x+15)

㏒x×(x+15)

㏒(
`x^(2)`+15x)

The answer is ㏒(
`x^(2)`+15x)

33. 2^(x-5) = 8

2^(x-5) = 2^3

Using property 2^a = 2^b

Then a = b

∴x-5 = 3

x = 8

The answer is x = 8

35. 2^x = 10

Taking log on both sides gives

㏒2^x = ㏒10

x×㏒2 = ㏒10

x = ㏒10/㏒2

The answer is x = ㏒10/㏒2

37. 8^-x = 12

Taking log on both sides gives

㏒8^-x = ㏒12

-x×㏒8 = ㏒12

x = -㏒12/㏒8

The answer is x = -㏒12/㏒8

39. 5(2^3 × x) = 8

5(8×x) = 8

x = 5

The answer is x=5