Rewrite 512^{4/3}=4096 in logarithmic form.

log_{4096}4/3=512

log_{512}4096=4/3

log_{4/3}4096=512

log_{512}4/3=4096

y=log_{a}x and x=a^{y }are equivalent

Therefore, since 512^{4/3}=4096, we know that in logarithmic form it would be 4/3=log_{512}4096