What is expand log_{4}(6(7^2)^3) ?

The solution to expand log_{4}(6(7^2)^3) is log_{4}(6)+6log_{4}(7)

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expand log_{4}(6(7^2)^3)

expand

lo g_{4} (6 (7^{2})^{3})

lo g_{4} (6) + 6 lo g_{4} (7)

Decimal Notation

9.71454 \dots

Solution steps

lo g_{4} (6 (7^{2})^{3})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{4} (6 (7^{2})^{3}) = lo g_{4} (6) + lo g_{4} ((7^{2})^{3})

= lo g_{4} (6) + lo g_{4} ((7^{2})^{3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{4} ((7^{2})^{3}) = 3 lo g_{4} (7^{2})

= lo g_{4} (6) + 3 lo g_{4} (7^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{4} (7^{2}) = 2 lo g_{4} (7)

= lo g_{4} (6) + 3 \cdot 2 lo g_{4} (7)

Multiply the numbers:

3 \cdot 2 = 6

= lo g_{4} (6) + 6 lo g_{4} (7)

lo g_{2^{'}} (\frac{3}{2})

ln (\frac{0.51}{1.02})

3.2 ln (4.92) - 5 ln (17.9)

ln (4) - ln (\frac{7}{2})

- lo g_{10} (0.7 \cdot 1 0^{- 3})

What is expand log_{4}(6(7^2)^3) ?
The solution to expand log_{4}(6(7^2)^3) is log_{4}(6)+6log_{4}(7)