Question

When utilizing technology to evaluate the solution for
5
⋅
2
2
t
=
3,375
, which logarithmic expression is appropriate for direct computation of
t
?




2
t
=
log
10
3,375
5
log
10
2






t
=
log
10
3,375
2
log
10
2






log
10
(
5
⋅
2
2
t
)
=
3,375






log
2
(
5
⋅
3,375
)
=
2
t

Answer 1

Start with 5·2^{2t} = 3375. Divide by 5: 2^{2t} = 3375/5 = 675. Take logs:

2t·log 2 = log(675) so t = log(675) / (2 log 2).

Equivalently t = [log(3375) − log(5)] / (2 log 2) or using natural logs t = ln(675) / (2 ln 2). Numerically t ≈ 4.699.