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

Sum

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

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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 1.2

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

Express the following in terms of log 2 and log 3: log 36

Express the following in terms of log 5 and/or log 2: log125

Write the logarithmic equation for:

F = `"G"("m"_1"m"_2)/"d"^2`

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

Express the following as a single logarithm:

`2 "log" 3 - (1)/(2) "log" 16 + "log" 12`

Simplify the following:

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

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: log 12

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

Simplify: log a² + log a^-1