What is ln(cos(5^x)5^xln(5)) ?

The solution to ln(cos(5^x)5^xln(5)) is ln(cos(5^x))+xln(5)+ln(ln(5))

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simplify ln(cos(5^x)5^xln(5))

simplify

ln (cos (5^{x}) 5^{x} ln (5))

ln (cos (5^{x})) + x ln (5) + ln (ln (5))

Solution steps

ln (cos (5^{x}) \cdot 5^{x} ln (5))

Apply log rule:

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

ln (cos (5^{x}) \cdot 5^{x} ln (5)) = ln (cos (5^{x})) + ln (5^{x}) + ln (ln (5))

= ln (cos (5^{x})) + ln (5^{x}) + ln (ln (5))

Apply log rule:

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

ln (5^{x}) = x ln (5)

= ln (cos (5^{x})) + x ln (5) + ln (ln (5))

ln (x - 6) - ln (x + 6)

ln (\frac{1}{2}) \cdot 20

ln (\frac{8235744}{8831079})

ln (x) - ln (x)

ln (2 y - 1) - ln (y - 1)

What is ln(cos(5^x)5^xln(5)) ?
The solution to ln(cos(5^x)5^xln(5)) is ln(cos(5^x))+xln(5)+ln(ln(5))