Question 37537
<pre><font size = 4><b>1) 0.04^log(base 0.2)3 
2) 10^1+ln5


0.04<sup>log<sub>0.2</sub>3</sup> 

0.04 can be written in terms of the base 0.2, that is,

0.04 = (0.2)˛

So substitute (0.2)˛ for 0.04

[(0.2)˛]<sup>log<sub>0.2</sub>3</sup>

Remove the brackets by multiplying the exponents 2 and log<sub>0.2</sub>3

(0.2)<sup>2·log<sub>0.2</sub>3</sup>

Use this rule of logarithms in the exponent:   A·log<sub>B</sub>C = log<sub>B</sub>C<sup>A</sup>

(0.2)<sup>log<sub>0.2</sub>3˛</sup>  

Substitute 9 for 3˛

(0.2)<sup>log<sub>0.2</sub>9</sup>

Use this rule of logarithms:  B<sup>log<sub>B</sub>A</sup> = A

Answer: 9


2) 10<sup>1+ln5</sup>



You can't simplify that, so I'd just punch it into a calculator
and give the decimal value

                406.8533651

Edwin
AnlytcPhil@aol.com</pre>