Solve the equation 35x 3 12 Give an exact answer in terms o

Solve the equation: 3^-5x - 3 12. Give an exact answer (in terms of natural logarithms); then round off to one decimal place.

Solution:

Given Equation

3^(-5x-3) = 12

Apply log On Both Sides

log(3^(-5x-3) ) = log12

(-5x-3) log3 = log12

Divide on Both Sides By log3

(-5x-3) log3/log3 = log12/log3

(-5x-3) = log12/log3

Add 3 on both sides

(-5x-3) + 3 = log12/log3 + 3

-5x = log12/log3 + 3

Divide both sides by -5

-5x/-5 = (log12/log3 + 3)/-5

x = - (log12/log3 + 3)/5

log12/log3 + 3

log12/log3 + 3/1

= log12/log3 + 3log3/log3

= (log12+3log3)log3

= (log12+log(3)³)log3

= (log12 . 3³)/log3

= log(324)/log3

= log(18²)/log3

= 2log18/log3

Substitute on above equation

x = - (2log18/log3)/5

x = - 2log18/5log3

x = - 1.05237