What is e^{3x}cosh(8x^3)-log_{7}(9x^2) ?

The solution to e^{3x}cosh(8x^3)-log_{7}(9x^2) is e^{3x}cosh(8x^3)-2log_{7}(3)-2log_{7}(x)

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simplify e^{3x}cosh(8x^3)-log_{7}(9x^2)

simplify

e^{3 x} cosh (8 x^{3}) - lo g_{7} (9 x^{2})

e^{3 x} cosh (8 x^{3}) - 2 lo g_{7} (3) - 2 lo g_{7} (x)

Solution steps

e^{3 x} cosh (8 x^{3}) - lo g_{7} (9 x^{2})

Apply log rule:

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

lo g_{7} (9 x^{2}) = lo g_{7} (9) + lo g_{7} (x^{2})

= e^{3 x} cosh (8 x^{3}) - (lo g_{7} (x^{2}) + lo g_{7} (9))

Apply log rule:

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

lo g_{7} (x^{2}) = 2 lo g_{7} (x)

= e^{3 x} cosh (8 x^{3}) - (lo g_{7} (9) + 2 lo g_{7} (x))

lo g_{7} (9) = 2 lo g_{7} (3)

= e^{3 x} cosh (8 x^{3}) - (2 lo g_{7} (x) + 2 lo g_{7} (3))

- (2 lo g_{7} (3) + 2 lo g_{7} (x)) : - 2 lo g_{7} (3) - 2 lo g_{7} (x)

= e^{3 x} cosh (8 x^{3}) - 2 lo g_{7} (3) - 2 lo g_{7} (x)

lo g_{2} (\frac{4}{x + 6})

4 ln (4 x)

ln (11) + 3 ln (x) - 9 ln (y)

lo g_{3} (5) - lo g_{3} (8)

lo g_{4} (\frac{16}{x ^{4}})

What is e^{3x}cosh(8x^3)-log_{7}(9x^2) ?
The solution to e^{3x}cosh(8x^3)-log_{7}(9x^2) is e^{3x}cosh(8x^3)-2log_{7}(3)-2log_{7}(x)