What is log_{e}((49pi^6)/3) ?

The solution to log_{e}((49pi^6)/3) is 2ln(7)+6ln(pi)-ln(3)

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simplify log_{e}((49pi^6)/3)

simplify

lo g_{e} (\frac{49 π ^{6}}{3})

2 ln (7) + 6 ln (π) - ln (3)

Decimal Notation

9.66158 \dots

Solution steps

lo g_{e} (\frac{49 π ^{6}}{3})

Apply log rule:

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

lo g_{e} (\frac{49 π ^{6}}{3}) = lo g_{e} (49 π^{6}) - lo g_{e} (3)

= lo g_{e} (49 π^{6}) - lo g_{e} (3)

Apply log rule:

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

lo g_{e} (49 π^{6}) = lo g_{e} (49) + lo g_{e} (π^{6})

= lo g_{e} (49) + lo g_{e} (π^{6}) - lo g_{e} (3)

Apply log rule:

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

lo g_{e} (π^{6}) = 6 lo g_{e} (π)

= lo g_{e} (49) + 6 lo g_{e} (π) - lo g_{e} (3)

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (49) + 6 lo g_{e} (π) - lo g_{e} (3)

Simplify

lo g_{e} (π) : ln (π)

= ln (49) + 6 ln (π) - lo g_{e} (3)

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (49) + 6 ln (π) - ln (3)

ln (49) = 2 ln (7)

= 2 ln (7) + 6 ln (π) - ln (3)

3 ln (x + 7) - ln (x + 8)

2 ln (x - 1) + 2 ln (y + 1)

ln (t^{2} x^{α} y^{β})

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

- lo g_{10} (9.2 \cdot 1 0^{- 2})

What is log_{e}((49pi^6)/3) ?
The solution to log_{e}((49pi^6)/3) is 2ln(7)+6ln(pi)-ln(3)