What is 1/2 (ln(2)+2ln(x)+5ln(m)-H) ?

The solution to 1/2 (ln(2)+2ln(x)+5ln(m)-H) is 1/2 (ln(2x^2m^5)-H)

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simplify 1/2 (ln(2)+2ln(x)+5ln(m)-H)

simplify

\frac{1}{2} (ln (2) + 2 ln (x) + 5 ln (m) - H)

\frac{1}{2} (ln (2 x^{2} m^{5}) - H)

Solution steps

\frac{1}{2} (ln (2) + 2 ln (x) + 5 ln (m) - H)

Apply log rule:

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

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

= \frac{1}{2} (ln (x^{2}) + 5 ln (m) + ln (2) - H)

Apply log rule:

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

ln (2) + ln (x^{2}) = ln (2 x^{2})

= \frac{1}{2} (ln (2 x^{2}) + 5 ln (m) - H)

Apply log rule:

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

5 ln (m) = ln (m^{5})

= \frac{1}{2} (ln (2 x^{2}) + ln (m^{5}) - H)

Apply log rule:

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

ln (2 x^{2}) + ln (m^{5}) = ln (2 x^{2} m^{5})

= \frac{1}{2} (ln (2 x^{2} m^{5}) - H)

\frac{1}{2 π \cdot 3} \cdot ln (\frac{0.1216}{0.0323})

2 lo g_{c} (z + 3) + lo g_{c} (3 z + 4)

ln (e^{4 x} (\frac{x ^{5} - 8 x + 6}{cos ( x )}))

\frac{1}{4} [3 ln (x + 7) - ln (x) - ln (x^{2} - 25)]

What is 1/2 (ln(2)+2ln(x)+5ln(m)-H) ?
The solution to 1/2 (ln(2)+2ln(x)+5ln(m)-H) is 1/2 (ln(2x^2m^5)-H)