What is (sqrt(1+3^x))^{ln(x^2)} ?

The solution to (sqrt(1+3^x))^{ln(x^2)} is (3^x+1)^{ln(x)}

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simplify (sqrt(1+3^x))^{ln(x^2)}

simplify

(1 + 3^{x})^{l n (x^{2})}

(3^{x} + 1)^{l n (x)}

Solution steps

(1 + 3^{x})^{l n (x^{2})}

Apply radical rule:

a = a^{\frac{1}{2}}

= ((1 + 3^{x})^{\frac{1}{2}})^{l n (x^{2})}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

= (1 + 3^{x})^{\frac{1}{2} l n (x^{2})}

Simplify

\frac{1}{2} ln (x^{2}) : \frac{ln ( x ^{2} )}{2}

= (1 + 3^{x})^{\frac{l n ( x ^{2} )}{2}}

\frac{ln ( x ^{2} )}{2} = ln (x)

= (1 + 3^{x})^{l n (x)}

0.24 x 1 0^{- 0.24 x^{60}}

(\frac{x}{3})^{3}

2 \cdot y

e^{- 0.36727}

9.105 \cdot 1 0^{- 2}

What is (sqrt(1+3^x))^{ln(x^2)} ?
The solution to (sqrt(1+3^x))^{ln(x^2)} is (3^x+1)^{ln(x)}