Express the Following in Terms of Log 5 And/Or Log 2: Log250 - Mathematics

Express the following in terms of log 5 and/or log 2: log250

Sum

log250
= log (5³ x 2)
= log 5³ + log2
= 3log 5 + log2.

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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 2.6

If log₅ x = y, find 5^{2y+ 3} in terms of x.

Prove that:

log₁₀ 125 = 3(1 - log₁₀2).

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 648

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

Express the following as a single logarithm:

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

Simplify the following:

`2 "log" 5 +"log" 8 - (1)/(2) "log" 4`

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 4 = 0.6020, find the value of each of the following: log8

If x² + y² = 6xy, prove that `"log"((x - y)/2) = (1)/(2)` (log x + log y)