Express the Following in Terms of Log 5 And/Or Log 2: Log500 - Mathematics

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

Sum

log500
= log (2² x 5³)
= log 2²+ log 5³
= 2 log 2 + 3 log 5.

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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 2.5

If x = (100)^a , y = (10000)^b and z = (10)^c , find log`(10sqrty)/( x^2z^3)` in terms of a, b and c.

If log 2 = 0.3010 and log 3 = 0.4771 ; find the value of : log 12

Given: log₃ m = x and log₃n = y.

Write down `3^(1 - 2y + 3x)` in terms of m and n.

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

Express the following in terms of log 2 and log 3: log 144

Write the logarithmic equation for:

V = `(1)/("D"l) sqrt("T"/(pi"r")`

Express the following as a single logarithm:

`2"log"(9)/(5) - 3"log"(3)/(5) + "log"(16)/(20)`

Simplify the following:

`3"log" (32)/(27) + 5 "log"(125)/(24) - 3"log" (625)/(243) + "log" (2)/(75)`

If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: log540

Find the value of:

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