en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(8x)-ln(x)

Solution

simplify

ln (8 x) - ln (x)

Solution

3 ln (2)

+1

Decimal Notation

2.07944 \dots

Solution steps

ln (8 x) - ln (x)

Apply log rule:

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

ln (8 x) - ln (x) = ln (\frac{8 x}{x})

= ln (\frac{8 x}{x})

Cancel the common factor:

x

= ln (8)

Rewrite

8

in power-base form:

8 = 2^{3}

= ln (2^{3})

Apply log rule:

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

ln (2^{3}) = 3 ln (2)

= 3 ln (2)

Popular Examples

simplify ln(a)-(ln(b)+ln(c))simplify

ln (a) - (ln (b) + ln (c))

expand log_{10}(y/(7x))expand

lo g_{10} (\frac{y}{7 x})

simplify ln(((1216.391509))/(11))simplify

ln (\frac{( 1216.391509 )}{11})

expand log_{10}(t/8)expand

lo g_{10} (\frac{t}{8})

simplify ln(a+b)+3ln(a-b)-4ln(c)simplify

ln (a + b) + 3 ln (a - b) - 4 ln (c)

Frequently Asked Questions (FAQ)

What is ln(8x)-ln(x) ?
The solution to ln(8x)-ln(x) is 3ln(2)