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Popular >

simplify 7ln(219)+18-7ln(3)+6

Solution

simplify

7 ln (219) + 18 - 7 ln (3) + 6

Solution

7 ln (73) + 24

+1

Decimal Notation

54.03321 \dots

Solution steps

7 ln (219) + 18 - 7 ln (3) + 6

Apply log rule:

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

7 ln (219) = ln (21 9^{7})

= ln (21 9^{7}) + 18 - 7 ln (3) + 6

Apply log rule:

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

7 ln (3) = ln (3^{7})

= ln (21 9^{7}) + 18 - ln (3^{7}) + 6

Apply log rule:

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

ln (21 9^{7}) - ln (3^{7}) = ln (\frac{21 9 ^{7}}{3 ^{7}})

= ln (\frac{21 9 ^{7}}{3 ^{7}}) + 18 + 6

\frac{21 9 ^{7}}{3 ^{7}} = 7 3^{7}

= ln (7 3^{7}) + 18 + 6

Apply log rule

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

assuming

x \geq 0

= 7 ln (73) + 18 + 6

Add the numbers:

18 + 6 = 24

= 7 ln (73) + 24

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Frequently Asked Questions (FAQ)

What is 7ln(219)+18-7ln(3)+6 ?
The solution to 7ln(219)+18-7ln(3)+6 is 7ln(73)+24