If Log 2 = X and Log 3 = Y, Find the Value of Each of the Following on Terms of X and Y: Log60

If log 2 = x and log 3 = y, find the value of each of the following on terms of x and y: log60

Sum

log60
= log (2 x 3 x 10)
= log 2 + log 3 + log 10
= x + y + 1.

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Expansion of Expressions with the Help of Laws of Logarithm

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Chapter 10: Logarithms - Exercise 10.2

Chapter 10 Logarithms
Exercise 10.2 | Q 21.1

Prove that : If a log b + b log a - 1 = 0, then b^a. a^b = 10

If log (a + 1) = log (4a - 3) - log 3; find a.

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: log250

Express the following in terms of log 2 and log 3: `"log" root(4)(648)`

Express the following as a single logarithm:

`2"log" (16)/(25) - 3 "log" (8)/(5) + "log" 90`

Simplify the following:

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

If 2 log x + 1 = 40, find: x

If log 27 = 1.431, find the value of the following: log300

Find the value of:

`("log"sqrt125 - "log"sqrt(27) - "log"sqrt(8))/("log"6 - "log"5)`