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Popular >

simplify ln(4x^bx^cx^{1-b-c})

Solution

simplify

ln (4 x^{b} x^{c} x^{1 - b - c})

Solution

ln (x) + 2 ln (2)

Solution steps

ln (4 x^{b} x^{c} x^{1 - b - c})

Apply log rule:

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

ln (4 x^{b} x^{c} x^{1 - b - c}) = ln (4) + ln (x^{b}) + ln (x^{c}) + ln (x^{1 - b - c})

= ln (4) + ln (x^{b}) + ln (x^{c}) + ln (x^{1 - b - c})

Apply log rule:

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

ln (x^{b}) = b ln (x)

= ln (4) + b ln (x) + ln (x^{c}) + ln (x^{1 - b - c})

Apply log rule:

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

ln (x^{c}) = c ln (x)

= ln (4) + b ln (x) + c ln (x) + ln (x^{1 - b - c})

Apply log rule:

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

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

= ln (4) + b ln (x) + c ln (x) + (1 - b - c) ln (x)

ln (4) = 2 ln (2)

= 2 ln (2) + b ln (x) + c ln (x) + ln (x) (1 - b - c)

= 2 ln (2) + b ln (x) + c ln (x) + ln (x) (1 - b - c)

Expand

ln (x) (1 - b - c) : ln (x) - b ln (x) - c ln (x)

= 2 ln (2) + b ln (x) + c ln (x) + ln (x) - b ln (x) - c ln (x)

Simplify

2 ln (2) + b ln (x) + c ln (x) + ln (x) - b ln (x) - c ln (x) : ln (x) + 2 ln (2)

= ln (x) + 2 ln (2)

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Frequently Asked Questions (FAQ)

What is ln(4x^bx^cx^{1-b-c}) ?
The solution to ln(4x^bx^cx^{1-b-c}) is ln(x)+2ln(2)