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受欢迎的代数 >

n(x)=log_{2/e}(x)

解答

n (x) = lo g_{\frac{2}{e}} (x)

解答

x = - \frac{W ( - ( ln ( 2 ) - 1 ) n )}{( ln ( 2 ) - 1 ) n}

求解步骤

n (x) = lo g_{\frac{2}{e}} (x)

若

f (x) = g (x)

，则

a^{f (x)} = a^{g (x)}

(\frac{2}{e})^{n x} = (\frac{2}{e})^{l o g_{\frac{2}{e}} (x)}

化简

(\frac{2}{e})^{l o g_{\frac{2}{e}} (x)} : x

(\frac{2}{e})^{n x} = x

解

(\frac{2}{e})^{n x} = x : x = - \frac{W ( - ( ln ( 2 ) - 1 ) n )}{( ln ( 2 ) - 1 ) n}

x = - \frac{W ( - ( ln ( 2 ) - 1 ) n )}{( ln ( 2 ) - 1 ) n}

验证解:

x = - \frac{W ( - ( ln ( 2 ) - 1 ) n )}{( ln ( 2 ) - 1 ) n}

真

解是

x = - \frac{W ( - ( ln ( 2 ) - 1 ) n )}{( ln ( 2 ) - 1 ) n}

作图

流行的例子

lo g_{2} (1 + a) = 4

335=log_{93}(x)

335 = lo g_{93} (x)

ln(16x)=ln(16)+4ln(2)

ln (16 x) = ln (16) + 4 ln (2)

log_{3}((x+3)/2)=2

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

log_{2}(x+6)-log_{2}(x-6)=3

lo g_{2} (x + 6) - lo g_{2} (x - 6) = 3