Use logarithms to solve the given equation: 2(1.08^5x + 1) = 13?

Question

can some one help with this question? i'm completely lost?

Answer 1

2*(1.08^5x +1)=13 . . .

1.08^5x +1=6.5

1.08^5x=5.5

log(1.08^5x)=log(5.5)

5x*log(1.08)=log(5.5)

x=log(5.5)/ [5*log(1.08)]

=0.740362689/ [5*0.033423755]

=0.740362689/0.167118777

x=4.4301586

Answer 2

1.08^5x+1=13/2=6.5.

INTERPRETATION 1:

1.08^5x=6.5-1=5.5.

5xlog(1.08)=log(5.5).

x=log(5.5)/5log(1.08)=4.4302 approx.

INTERPRETATION 2:

If the question involved 1.08^(5x+1), then 5x+1=log(6.5)/log(1.08)=24.3214, making x=23.3214/5=4.6643 approx.

Answer 3

2(1.08^5x)= 13

11.08^5x =5.5

log          (5.5)    = 5x   (log of 5.5 with base 1.08 is 5x )

     ( 1.08)

log of 5.5 with base 1.08 =22.1508

x = 22.1508/5

x =4.43016