log₇ (⁵√7. √7) - log₃ (³√3) + log₄ 2 = ?

log₇ (⁵√7. √7) – log₃ (³√3) + log₄ 2
= log₇7^{(1/5 + 1/2)} - log₃3^1/3 + log₄4^1/2
= 7/10 log₇7 – 1/3 log₃3 + 1/2log₄4
= 7/10 – 1/3 + 1/2
= 26/30
= 13/15