Question

(2log³10-½log³25):(log³1:20)​

Answer 1

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Answer 2

To simplify the expression (2log³10 - ½log³25) divided by (log³1:20), you can use the properties of logarithms.

1. Start with the expression: (2log³10 - ½log³25) / (log³1:20)

2. Use the properties of logarithms to simplify each term in the numerator:

   • 2log³10 = log³(10²) = log³100
   • ½log³25 = log³(25^(1/2)) = log³5

3. Substitute these simplified terms back into the expression: (log³100 - log³5) / (log³1:20)

4. Use the properties of logarithms to combine the terms in the numerator: log³(100/5) / (log³1:20)

5. Simplify further: log³(20) / (log³1:20)

Now, you have simplified the expression to log base 3 of 20 divided by log base 3 of 1:20. This expression cannot be simplified further without knowing the value of log³1:20, so the final result is:

log³(20) / log³(1:20)