What is ln(1n(5x)^{ln(3x)}) ?

The solution to ln(1n(5x)^{ln(3x)}) is ln(3x)ln(5x)+ln(n)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(1n(5x)^{ln(3x)})

simplify

ln (1 n (5 x)^{l n (3 x)})

ln (3 x) ln (5 x) + ln (n)

Solution steps

ln (1 \cdot n (5 x)^{l n (3 x)})

Apply log rule:

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

ln (1 \cdot n (5 x)^{l n (3 x)}) = ln (1) + ln (n) + ln ((5 x)^{l n (3 x)})

= ln (1) + ln (n) + ln ((5 x)^{l n (3 x)})

Apply log rule:

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

ln ((5 x)^{l n (3 x)}) = ln (3 x) ln (5 x)

= ln (1) + ln (n) + ln (3 x) ln (5 x)

Apply log rule:

lo g_{a} (1) = 0

= 0 + ln (n) + ln (3 x) ln (5 x)

0 + ln (n) + ln (3 x) ln (5 x) = ln (n) + ln (3 x) ln (5 x)

= ln (3 x) ln (5 x) + ln (n)

4 ln (2 e)

ln (x) + ln (y)

ln (2 (3 + i)^{3})

\frac{12}{5} \cdot lo g_{2} (5)

ln (5) - ln (2) - \frac{3}{10}

What is ln(1n(5x)^{ln(3x)}) ?
The solution to ln(1n(5x)^{ln(3x)}) is ln(3x)ln(5x)+ln(n)