What is expand a^x*(ln(a)+x/a) ?

The solution to expand a^x*(ln(a)+x/a) is a^xln(a)+a^{x-1}x

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expand a^x*(ln(a)+x/a)

expand

a^{x} \cdot (ln (a) + \frac{x}{a})

a^{x} ln (a) + a^{x - 1} x

Solution steps

a^{x} (ln (a) + \frac{x}{a})

Apply the distributive law:

a (b + c) = ab + a c

a = a^{x}, b = ln (a), c = \frac{x}{a}

= a^{x} ln (a) + a^{x} \frac{x}{a}

a^{x} \frac{x}{a} = a^{x - 1} x

= a^{x} ln (a) + a^{x - 1} x

(P - J)^{2} + (Q - K)^{2}

(a + 55)^{2}

3 (1 + \frac{2 i}{n})^{2}

\frac{15 x ^{2} - 10 x + 16}{( 3 x - 1 ) ^{2}}

\frac{1}{y ( y - 1 )}

What is expand a^x*(ln(a)+x/a) ?
The solution to expand a^x*(ln(a)+x/a) is a^xln(a)+a^{x-1}x