What is expand log_{4}(3*5*8^4) ?

The solution to expand log_{4}(3*5*8^4) is log_{4}(3)+log_{4}(5)+6

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expand log_{4}(358^4)

expand

lo g_{4} (3 \cdot 5 \cdot 8^{4})

lo g_{4} (3) + lo g_{4} (5) + 6

Decimal Notation

7.95344 \dots

Solution steps

lo g_{4} (3 \cdot 5 \cdot 8^{4})

Apply log rule:

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

lo g_{4} (3 \cdot 5 \cdot 8^{4}) = lo g_{4} (3) + lo g_{4} (5) + lo g_{4} (8^{4})

= lo g_{4} (3) + lo g_{4} (5) + lo g_{4} (8^{4})

Apply log rule:

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

lo g_{4} (8^{4}) = 4 lo g_{4} (8)

= lo g_{4} (3) + lo g_{4} (5) + 4 lo g_{4} (8)

4 lo g_{4} (8) = 6

= lo g_{4} (3) + lo g_{4} (5) + 6

\frac{1}{2} \cdot lo g_{5} (324) - lo g_{5} (2)

4 ln (2) + 2 ln (x)

- (\frac{3}{9}) lo g_{2} (\frac{3}{9}) - (\frac{6}{9}) lo g_{2} (\frac{6}{9})

3 lo g_{2} (x) + \frac{1}{2} lo g_{2} (x + 1)

What is expand log_{4}(3*5*8^4) ?
The solution to expand log_{4}(3*5*8^4) is log_{4}(3)+log_{4}(5)+6