Express the Following in Terms of Log 2 and Log 3: Log 54

Express the following in terms of log 2 and log 3: log 54

बेरीज

log 54
= log (2 x 3 x 3 x 3)
= log (2 x 3³)
= log 2 + log 3³
= log 2 + 3 log 3.

shaalaa.com

Expansion of Expressions with the Help of Laws of Logarithm

या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

पाठ 7: Logarithms - Exercise 10.2

पाठ 7 Logarithms
Exercise 10.2 | Q 1.2

If log₁₀2 = a and log₁₀3 = b ; express each of the following in terms of 'a' and 'b': log 2.25

Given: log₃ m = x and log₃ n = y.
Express 3^{2x - 3} in terms of m.

Given `log_x 25 - log_x 5 = 2 - log_x (1/125)` ; find x.

Express the following in terms of log 5 and/or log 2: log500

Express the following in terms of log 2 and log 3: `"log"(26)/(51) - "log"(91)/(119)`

Express the following as a single logarithm:
log 144 - log 72 + log 150 - log 50

Express the following as a single logarithm:

`2"log"(15)/(18) - "log"(25)/(162) + "log"(4)/(9)`

Express the following as a single logarithm:

`(1)/(2)"log"25 - 2"log"3 + "log"36`

Simplify the following:

`12"log" (3)/(2) + 7 "log" (125)/(27) - 5 "log" (25)/(36) - 7 "log" 25 + "log" (16)/(3)`

Find the value of:

`("log"sqrt(27) + "log"8 + "log"sqrt(1000))/("log"120)`