Solve frac{x{5}^sqrt{x}ln(5)}{2sqrt{x}}+{5}^sqrt{x}

$$\frac{ x { 5 }^{ \sqrt{ x } } \ln ( 5 ) }{ 2 \sqrt{ x } } + { 5 }^{ \sqrt{ x } }$$

Factor

$$\frac{\left(\ln(5)\sqrt{x}+2\right)\times 5^{\sqrt{x}}}{2}$$

Solution Steps

Factor the expressions that are not already factored in \frac{x\times 5^{\sqrt{x}}\log_{e}\left(5\right)}{2\sqrt{x}}.

$$factor(\frac{\ln(5)\times \frac{1}{\ln(e)}x\times 5^{\sqrt{x}}}{2\sqrt{x}}+5^{\sqrt{x}})$$

Cancel out \sqrt{x} in both numerator and denominator.

$$factor(\frac{\ln(5)\times \frac{1}{\ln(e)}\sqrt{x}\times 5^{\sqrt{x}}}{2}+5^{\sqrt{x}})$$

The natural logarithm of e is 1.

$$factor(\frac{\ln(5)\times \frac{1}{1}\sqrt{x}\times 5^{\sqrt{x}}}{2}+5^{\sqrt{x}})$$

Anything divided by one gives itself.

$$factor(\frac{\ln(5)\times 1\sqrt{x}\times 5^{\sqrt{x}}}{2}+5^{\sqrt{x}})$$

Factor out \frac{1}{2}.

$$\frac{\ln(5)\sqrt{x}\times 5^{\sqrt{x}}+2\times 5^{\sqrt{x}}}{2}$$

Consider \ln(5)\sqrt{x}\times 5^{\sqrt{x}}+2\times 5^{\sqrt{x}}. Factor out 5^{\sqrt{x}}.

$$5^{\sqrt{x}}\left(\ln(5)\sqrt{x}+2\right)$$

Rewrite the complete factored expression.

$$\frac{5^{\sqrt{x}}\left(\ln(5)\sqrt{x}+2\right)}{2}$$

Evaluate

$$\frac{\left(\ln(5)\sqrt{x}+2\right)\times 5^{\sqrt{x}}}{2}$$