What is simplify-ln(x)+1/2 ln(b)-ln(c) ?

The solution to simplify-ln(x)+1/2 ln(b)-ln(c) is ln((b^{1/2})/(cx))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-ln(x)+1/2 ln(b)-ln(c)

simplify

- ln (x) + \frac{1}{2} ln (b) - ln (c)

ln (\frac{b ^{\frac{1}{2}}}{c x})

Solution steps

- ln (x) + \frac{1}{2} ln (b) - ln (c)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} ln (b) = ln (b^{\frac{1}{2}})

= - ln (x) + ln (b^{\frac{1}{2}}) - ln (c)

Apply log rule:

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

ln (b^{\frac{1}{2}}) - ln (x) = ln (\frac{b ^{\frac{1}{2}}}{x})

= ln (\frac{b ^{\frac{1}{2}}}{x}) - ln (c)

Apply log rule:

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

ln (\frac{b ^{\frac{1}{2}}}{x}) - ln (c) = ln \frac{\frac{b ^{\frac{1}{2}}}{x}}{c}

= ln \frac{\frac{b ^{\frac{1}{2}}}{x}}{c}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= ln (\frac{b ^{\frac{1}{2}}}{c x})

ln (\frac{e ^{9}}{19})

ln (\frac{x}{( x + 2 ) ( x + 3 )})

ln (\frac{x ^{2} x ^{2} + 3}{( x + 3 ) ^{8}})

ln (30) + 2 ln (y) + ln (x)

ln (\frac{1 + x}{x})

What is simplify-ln(x)+1/2 ln(b)-ln(c) ?
The solution to simplify-ln(x)+1/2 ln(b)-ln(c) is ln((b^{1/2})/(cx))