Solve 2log 9(3)-4log 9(3) log 9(1/729)

Evaluate

2 lo g_{10} (9) \times 3 - 4 lo g_{10} (9) \times 3 lo g_{10} (9) \times \frac{1}{729}

Multiply the terms

6 lo g_{10} (9) - 4 lo g_{10} (9) \times 3 lo g_{10} (9) \times \frac{1}{729}

Multiply

More Steps

6 lo g_{10} (9) - \frac{4 ( lo g _{10} ( 9 ) ) ^{2}}{243}

Simplify

More Steps

6 \times 2 lo g_{10} (3) - \frac{4 ( lo g _{10} ( 9 ) ) ^{2}}{243}

Simplify

More Steps

6 \times 2 lo g_{10} (3) - \frac{4 ( 2 lo g _{10} ( 3 ) ) ^{2}}{243}

Rewrite the expression

12 lo g_{10} (3) - \frac{4 ( 2 lo g _{10} ( 3 ) ) ^{2}}{243}

Evaluate the power

More Steps

12 lo g_{10} (3) - \frac{16 ( lo g _{10} ( 3 ) ) ^{2}}{243}

Reduce fractions to a common denominator

\frac{12 lo g _{10} ( 3 ) \times 243}{243} - \frac{16 ( lo g _{10} ( 3 ) ) ^{2}}{243}

Write all numerators above the common denominator

\frac{12 lo g _{10} ( 3 ) \times 243 - 16 ( lo g _{10} ( 3 ) ) ^{2}}{243}

Solution

\frac{2916 lo g _{10} ( 3 ) - 16 ( lo g _{10} ( 3 ) ) ^{2}}{243}

Alternative Form

\approx 5.710466

Calculate the value