What is join 10^{1/2}log_{10}(5) ?

The solution to join 10^{1/2}log_{10}(5) is log_{10}(5^{10^{1/2}})

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join 10^{1/2}log_{10}(5)

join

1 0^{\frac{1}{2}} lo g_{10} (5)

lo g_{10} (5^{1 0^{\frac{1}{2}}})

Decimal Notation

2.21033 \dots

Solution steps

1 0^{\frac{1}{2}} lo g_{10} (5)

Apply log rule:

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

1 0^{\frac{1}{2}} lo g_{10} (5) = lo g_{10} (5^{1 0^{\frac{1}{2}}})

= lo g_{10} (5^{1 0^{\frac{1}{2}}})

ln (x^{2} y^{3})

- lo g_{10} (5.3 \cdot 1 0^{- 8})

ln (x y^{2} z^{- 4})

6.1 + lo g_{10} (\frac{13}{12.2})

ln (\frac{100}{96.87})

What is join 10^{1/2}log_{10}(5) ?
The solution to join 10^{1/2}log_{10}(5) is log_{10}(5^{10^{1/2}})