What is log_{10}(1/(e^2sqrt(e))) ?

The solution to log_{10}(1/(e^2sqrt(e))) is -5/2 log_{10}(e)

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simplify log_{10}(1/(e^2sqrt(e)))

simplify

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

- \frac{5}{2} lo g_{10} (e)

Decimal Notation

- 1.08573 \dots

Solution steps

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

Apply log rule:

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

lo g_{10} (\frac{1}{e ^{2} e}) = lo g_{10} (1) - lo g_{10} (e^{2} e)

= lo g_{10} (1) - lo g_{10} (e^{2} e)

Apply log rule:

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

lo g_{10} (e^{2} e) = lo g_{10} (e^{2}) + lo g_{10} (e)

= lo g_{10} (1) - (lo g_{10} (e^{2}) + lo g_{10} (e))

Apply log rule:

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

lo g_{10} (e^{2}) = 2 lo g_{10} (e)

= lo g_{10} (1) - (2 lo g_{10} (e) + lo g_{10} (e))

lo g_{10} (1) = 0

- (2 lo g_{10} (e) + lo g_{10} (e)) = - \frac{5}{2} lo g_{10} (e)

= 0 - \frac{5}{2} lo g_{10} (e)

0 - \frac{5}{2} lo g_{10} (e) = - \frac{5}{2} lo g_{10} (e)

= - \frac{5}{2} lo g_{10} (e)

5 lo g_{4} (a) - 10 lo g_{4} (b)

\frac{1}{6} lo g_{2} (\frac{1}{6}) + \frac{5}{6} lo g_{2} (\frac{5}{6})

ln (a rc T g (1 + x^{2}))

3 lo g_{10} (x) + lo g_{10} (3)

8 ln (x) - 4 ln (5)

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