Write the exact answer using base 10 or base e log

Question

8^-x+6=17^-5x

Answer 1

8^(-x+6) = 17^(-5x)

take log base 17 of both sides

(-x+6)log₁₇8 = -5x

(-x+6)ln8/ln17 = -5x

(-x+6).734 =-5x

-.734+5x = -6(.734)

4.266x = -4.404

x = -4.404/4.266 = -1.0323

or for the EXACT solution:

-xln8 + 6ln8 = -5xln17

5xln17-xln8 = -6ln8

x(5ln17-ln8) =-6ln8

x = Exactly 6ln8/(ln8-5ln17)

x=6(2.08)/(2.08-14.17)

x=12.48/-12.09

x =about -1.032

8^(-x+6) = 17^-5x

8^(1.-032+6) = 17^-5(-1.032)

8^7.032 = 17^5.16

2,2x10^6 = 2.2x10^6

or

8^(-x+6) = 17^-5x

take log to the base 8 of both sides

-x+6 = -5xlog₈17

-x+6 =-5ln17/ln8

ln8(-x+6) =-5xln17

-xln8 +6ln8 = -5xln17

5xln17-xln8 =-6ln8

x(5ln17-ln8) =-6ln8

x = -6ln8/(5ln17-ln8)

x = exactly 6ln8/(ln8-5ln17)

x= about -1.032

or using log to the base 10, common logs

x= exactly 6log8/(log8 -5log17)

x = about 6(.903)/(.903-5(12.304))

= 54.18/(.903-61.52)

=54.18/-52.49

= about -1.032