Question

Rewrite the expression.

Answer 1

Log₄8 + 3 · log₄x

so the easiest way to do this is to note that these logs are separated by an addition symbol--it isn't "log₄8 + 3" times "log₄x"

log₄8
plus
3 · log₄x

for the second log, you can condense it with log properties/rules: the coefficient out front, when you condense it, becomes the exponent for the argument of your log:
3 · log₄x = log₄(x³)

so, having condensed that, your equation reads:

log₄8 + log₄(x³)

you could technically evaluate the first log, but the question wants both of these to become a single logarithm, which means you want to combine them. log properties state that if logs are being added, you can multiply their arguments (for example: logₓab = logₓa + logₓb)

you just want to apply that property to this, so you'll be multiplying your arguments 8 and x³:

log₄(8x³) is the answer, expressed as one logarithm.