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

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

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join 2^{pi/2}log_{10}(2)

join

2^{\frac{π}{2}} lo g_{10} (2)

lo g_{10} (2^{2^{\frac{π}{2}}})

Decimal Notation

0.89426 \dots

Solution steps

2^{\frac{π}{2}} lo g_{10} (2)

Apply log rule:

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

2^{\frac{π}{2}} lo g_{10} (2) = lo g_{10} (2^{2^{\frac{π}{2}}})

= lo g_{10} (2^{2^{\frac{π}{2}}})

- \frac{1}{8} (ln a + \frac{5}{2} - ln a + \frac{1}{2}) + C

ln (\frac{10}{22}) \cdot 5

ln (a \cdot b \cdot c)

- ln (5) - \frac{1}{4} ln (3)

ln (\frac{( x ^{5} \cdot z ^{5} )}{y ^{11} \cdot w ^{15}})

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