What is log_{5}(5e^{10}*125) ?

The solution to log_{5}(5e^{10}*125) is 10log_{5}(e)+4

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simplify log_{5}(5e^{10}*125)

simplify

lo g_{5} (5 e^{10} \cdot 125)

10 lo g_{5} (e) + 4

Decimal Notation

10.21334 \dots

Solution steps

lo g_{5} (5 e^{10} \cdot 125)

Apply log rule:

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

lo g_{5} (5 e^{10} \cdot 125) = lo g_{5} (5) + lo g_{5} (e^{10}) + lo g_{5} (125)

= lo g_{5} (5) + lo g_{5} (e^{10}) + lo g_{5} (125)

Apply log rule:

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

lo g_{5} (e^{10}) = 10 lo g_{5} (e)

= lo g_{5} (5) + 10 lo g_{5} (e) + lo g_{5} (125)

Apply log rule:

lo g_{a} (a) = 1

= 1 + 10 lo g_{5} (e) + lo g_{5} (125)

lo g_{5} (125) = 3

= 1 + 10 lo g_{5} (e) + 3

Add the numbers:

1 + 3 = 4

= 10 lo g_{5} (e) + 4

ln (3) + \frac{1}{2} ln (x + 2) - 5 ln (1 + x)

ln (x + 2) - ln (x^{2} + 2 x)

(2.5 \cdot ln (2) + ln (3)) \cdot 0.831

2000 (ln (140000) - ln (87500)) - 245

6 lo g_{4} (y - 5) - 5 lo g_{4} (y + 4)

What is log_{5}(5e^{10}*125) ?
The solution to log_{5}(5e^{10}*125) is 10log_{5}(e)+4