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Popular >

simplify 7ln(6)-7ln(3)

Solution

simplify

7 ln (6) - 7 ln (3)

Solution

7 ln (2)

+1

Decimal Notation

4.85203 \dots

Solution steps

7 ln (6) - 7 ln (3)

Apply log rule:

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

7 ln (6) = ln (6^{7})

= ln (6^{7}) - 7 ln (3)

Apply log rule:

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

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

= ln (6^{7}) - ln (3^{7})

Apply log rule:

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

ln (6^{7}) - ln (3^{7}) = ln (\frac{6 ^{7}}{3 ^{7}})

= ln (\frac{6 ^{7}}{3 ^{7}})

\frac{6 ^{7}}{3 ^{7}} = 128

= ln (128)

Rewrite

128

in power-base form:

128 = 2^{7}

= ln (2^{7})

Apply log rule:

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

ln (2^{7}) = 7 ln (2)

= 7 ln (2)

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Frequently Asked Questions (FAQ)

What is 7ln(6)-7ln(3) ?
The solution to 7ln(6)-7ln(3) is 7ln(2)