What is join 1/2 log_{10}(8+sqrt(65)) ?

The solution to join 1/2 log_{10}(8+sqrt(65)) is log_{10}((8+sqrt(65))^{1/2})

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join 1/2 log_{10}(8+sqrt(65))

join

\frac{1}{2} lo g_{10} (8 + 65)

lo g_{10} ((8 + 65)^{\frac{1}{2}})

Decimal Notation

0.60290 \dots

Solution steps

\frac{1}{2} lo g_{10} (8 + 65)

Apply log rule:

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

\frac{1}{2} lo g_{10} (8 + 65) = lo g_{10} ((8 + 65)^{\frac{1}{2}})

= lo g_{10} ((8 + 65)^{\frac{1}{2}})

ln (13) + 7 ln (a) - 11 ln (b) + ln (c)

lo g_{10} (0.48 5^{\frac{1}{4}} \cdot 0.3 6^{\frac{1}{3}})

ln (3 x) - 2 ln (x)

ln (a) + ln (\frac{1}{2 b}) - b (\frac{1}{2 b})^{2}

e lo g_{3} (\frac{1}{81}) + lo g_{\frac{1}{3}} (\frac{1}{61})_{e}

What is join 1/2 log_{10}(8+sqrt(65)) ?
The solution to join 1/2 log_{10}(8+sqrt(65)) is log_{10}((8+sqrt(65))^{1/2})