Need help with these logarithms questions! Thanks

Question

1. Write as a single log

2logx - log₁₁y + 1/2 log ₁₁z

 

2. Evaluate

3log₇4 -2log₇8

 

3. Expand

log_w(12a³/b²)

 

thank you soo much!!

Answer 1

You may have made a typo on question 1.  So I will go on to question 2.

 

 

2)

 

Apply the properties of logs.

 

Bring the coefficient of the logs as the exponent of the log bases.

 

log₇(4³) - log₇(8²)

 

 

Divide the arguments of the logs.

 

log₇(4³ / 8²) =

 

log₇(64 / 64) =

 

log₇(1)

 

 7 raised to what number results in 1?  That will be zero.

 

log₇(1) = 0

 

 

 

3)

 

log_w(12a³ / b²)

 

 

Subtract the logs.

 

log_w(12a³) - log_w(b²)

 

 

Expand the first term by adding the logs.

 

log_w(12) + log_w(a³) - log_w(b²)

 

 

Bring the exponents of the log terms as the coefficient of the logs.

 

log_w(12) + 3log_w(a) - 2log_w(b)