We are given the following equation:
[tex]14^{7-7v}=42[/tex]
To solve for "v" we will take logarithms on both sides:
[tex]\log 14^{7-7v}=\log 42[/tex]
Applying logarithm property:
[tex](7-7v)\log 14=\log 42[/tex]
Dividing both sides by "log 14":
[tex]7-7v=\frac{\log 42}{\log 14}[/tex]
Subtracting 7 to both sides:
[tex]-7v=\frac{\log 42}{\log 14}-7[/tex]
Dividing by -7 both sides
[tex]v=-\frac{1}{7}\frac{\log 42}{\log 14}+1[/tex]
Solving the operations:
[tex]v=0.79[/tex]
