What is log_{5}((sqrt(5))/(25))+e^{ln(3)+ln(4)} ?

The solution to log_{5}((sqrt(5))/(25))+e^{ln(3)+ln(4)} is log_{5}((sqrt(5))/(25))+12

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simplify log_{5}((sqrt(5))/(25))+e^{ln(3)+ln(4)}

simplify

lo g_{5} (\frac{5}{25}) + e^{l n (3) + l n (4)}

lo g_{5} (\frac{5}{25}) + 12

Decimal Notation

10.5

Solution steps

lo g_{5} (\frac{5}{25}) + e^{l n (3) + l n (4)}

Apply log rule:

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

ln (3) + ln (4) = ln (3 \cdot 4)

= lo g_{5} (\frac{5}{25}) + e^{l n (3 \cdot 4)}

Multiply the numbers:

3 \cdot 4 = 12

= lo g_{5} (\frac{5}{25}) + e^{l n (12)}

Apply log rule:

a^{l o g_{a} (b)} = b

= lo g_{5} (\frac{5}{25}) + 12

lo g_{b} (y^{6} z)

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

ln (x^{2} e^{x})

lo g_{10} (\frac{40}{9}) + 4 lo g_{10} (5) + 2 lo g_{10} (6)

2 - lo g_{5} (\frac{1}{16}) - \frac{1}{3} lo g_{5} (8)

What is log_{5}((sqrt(5))/(25))+e^{ln(3)+ln(4)} ?
The solution to log_{5}((sqrt(5))/(25))+e^{ln(3)+ln(4)} is log_{5}((sqrt(5))/(25))+12