Hello there. To solve this question, we'll need to remember how to apply the logarithms rules.
Given the exponential equation: 7^(-x/100) = 6.
Calculate the base 7 logarithm on both sides of the equality:
Now, apply the following rule: log(a^b) = b*log(a)
Then, remember that: log_a(a) = 1, such that:
Multiply both sides of the equation by a factor of -100
x = -100 log_7(6)
This is the solution for the a) question.
Now, using a calculator, we get that: log_7(6) approx. 0.92078222116
Multiplying this value by -100, we'll have:
x approx -92.078222116
In which we can round to 6 decimal places as:
x approx -92.078222
This is the solution for the b) question.