Answer:
[tex]x_{1} = \frac{4}{7} \\x_{2} = \frac{-4}{7} \\[/tex]
Step-by-step explanation:
To solve this equation, one must apply the following logarithmic property:
if
[tex]log_{a}(b) = c\\[/tex]
then
[tex]b= a^{c}[/tex]
Applying it to the problem at hand:
[tex]2^{4} = 49x^{2} \\x^{2} = \frac{16}{49} \\x_{1} = \frac{4}{7} \\x_{2} = \frac{-4}{7} \\[/tex]
The solutions to the problem are 4/7 and -4/7.
*Note that this solution was pretty straight forward because log2(16) = 4 is a known value, otherwise, a change of base to a base ten log would be required.
