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Popular >

simplify ln(2(1/9)^2)-18*1/9

Solution

simplify

ln (2 (\frac{1}{9})^{2}) - 18 \cdot \frac{1}{9}

Solution

ln (2) - 4 ln (3) - 2

+1

Decimal Notation

- 5.70130 \dots

Solution steps

ln (2 (\frac{1}{9})^{2}) - 18 \cdot \frac{1}{9}

Apply log rule:

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

ln (2 (\frac{1}{9})^{2}) = ln (2) + ln ((\frac{1}{9})^{2})

= ln (2) + ln ((\frac{1}{9})^{2}) - 18 \cdot \frac{1}{9}

Apply log rule:

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

ln ((\frac{1}{9})^{2}) = 2 ln (\frac{1}{9})

= ln (2) + 2 ln (\frac{1}{9}) - 18 \cdot \frac{1}{9}

Apply log rule:

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

ln (\frac{1}{9}) = ln (1) - ln (9)

= ln (2) + 2 (ln (1) - ln (9)) - 18 \cdot \frac{1}{9}

2 (ln (1) - ln (9)) = - 4 ln (3)

= ln (2) - 4 ln (3) - 18 \cdot \frac{1}{9}

18 \cdot \frac{1}{9} = 2

= ln (2) - 4 ln (3) - 2

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Frequently Asked Questions (FAQ)

What is ln(2(1/9)^2)-18*1/9 ?
The solution to ln(2(1/9)^2)-18*1/9 is ln(2)-4ln(3)-2