How to solve this log problem

let log_[b]10=Q, lob_[b]7=U

log_[b]sqt(10/343=

log_[b]sqrt(10/343)=0.5*log_[b](10/343)
=0.5*((log_[b]10)-(log_[b]343)
)=0.5*((log_[b]10)-(3log_[b]7))
because,log_[b]343=log_[b]7^3=3log_[b]7
hence substituting,the expression becomes,
=(Q-3U)/2

log_[b](√(10/343))
Take the square root out of the log (1/2 power):
½ log_[b](10/343)
Split the log into pieces:
½ log_[b](10) - ½ log_[b](343)
Simplify 343 into 7³
½ log_[b](10) - ½ log_[b](7³)
Pull the exponent out:
(1/2) log_[b](10) - (3/2) log_[b](7)
Replace with Q and U:
(1/2) Q - (3/2) U