What is the exact value of x?

Question

5⋅84x=376



x=log75.2/4log8

x=4log8/log75.2 <my answer

x=log84/log75.2

x=4log75.2/log8

Answer 1

not quite...

5⋅8^(4x) = 376
8^(4x) = 75.2
4x log8 = log75.2
x = log75.2/(4log8)

or, since 4log8 = log4096,

x = log₄₀₉₆75.2