If Log1025 = X and Log1027 = Y; Evaluate Without Using Logarithmic Tables, in Terms of X and Y: Log105

If log₁₀25 = x and log₁₀27 = y; evaluate without using logarithmic tables, in terms of x and y: log₁₀5

Sum

log₁₀25 = x
⇒ log₁₀5² =x
⇒ 2log₁₀5 = x
⇒ log₁₀5 = `x/(2)`.

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Expansion of Expressions with the Help of Laws of Logarithm

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Chapter 7: Logarithms - Exercise 10.2

Chapter 7 Logarithms
Exercise 10.2 | Q 18.1

Given 3log x + `1/2`log y = 2, express y in term of x.

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

Given: log₃ m = x and log₃n = y.

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

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

Express the following as a single logarithm:
log 18 + log 25 - log 30

Express the following as a single logarithm:

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

Simplify the following:

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

If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: log45

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

Simplify: log a² + log a^-1