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受欢迎的代数 >

化简 (log_{10}(9))/(log_{10)(4)}

解答

化简

\frac{lo g _{10} ( 9 )}{lo g _{10} ( 4 )}

解答

lo g_{2} (3)

+1

十进制

1.58496 \dots

求解步骤

\frac{lo g _{10} ( 9 )}{lo g _{10} ( 4 )}

lo g_{10} (9) = 2 lo g_{10} (3)

= \frac{2 lo g _{10} ( 3 )}{lo g _{10} ( 4 )}

使用对数计算法则:

\frac{lo g _{c} ( b )}{lo g _{c} ( a )} = lo g_{a} (b)

\frac{lo g _{10} ( 3 )}{lo g _{10} ( 4 )} = lo g_{4} (3)

= 2 lo g_{4} (3)

因式分解数字:

4 = 2^{2}

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

使用对数计算法则:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

lo g_{2^{2}} (3) = \frac{1}{2} lo g_{2} (3)

= 2 \cdot \frac{1}{2} lo g_{2} (3)

2 \cdot \frac{1}{2} lo g_{2} (3) = lo g_{2} (3)

= lo g_{2} (3)

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