Solve 5log50+2log48-5log2-2log3

Evaluate

5 lo g_{10} (50) + 2 lo g_{10} (48) - 5 lo g_{10} (2) - 2 lo g_{10} (3)

Add the terms

More Steps

lo g_{10} (2304 \times 5 0^{5}) - 5 lo g_{10} (2) - 2 lo g_{10} (3)

Add the numbers

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lo g_{10} (72 \times 5 0^{5}) - 2 lo g_{10} (3)

Rewrite the expression

lo g_{10} (72 \times 5 0^{5}) - lo g_{10} (3^{2})

Use the logarithm base change rule

lo g_{10} (72 \times 5 0^{5}) + lo g_{10} (3^{- 2})

Use the logarithm product rule

lo g_{10} (72 \times 5 0^{5} \times 3^{- 2})

Multiply the numbers

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lo g_{10} (8 \times 5 0^{5})

Use lo g_{a} (x \times y) = lo g_{a} (x) + lo g_{a} (y) to transform the expression

lo g_{10} (8) + lo g_{10} (5 0^{5})

Simplify the expression

More Steps

3 lo g_{10} (2) + lo g_{10} (5 0^{5})

Solution

3 lo g_{10} (2) + 5 lo g_{10} (50)

Alternative Form

\approx 9.39794

Calculate the value