Log Properties

Write log_b(xy) as two logs

• log_bx+log_by
• log_bx-log_by
• log_bx*log_by
• log_bx/log_by

Write log_b(x/y) as two logs

• log_bx-log_by
• log_bx+log_by
• log_bx*log_by
• log_bx/log_by

Rewrite log_b(xⁿ)

• nlog_bx
• (log_bx)ⁿ
• xⁿlog_bx
• log_b(xⁿ)

• 5log₆(a) + 6log₆(c) − 30log₆(b)
• log₆(a) + 6log₆(c) − 5log₆(b)
• 6log₆(a) − 6log₆(c) − 30log₆(b)
• 6log₆(a) + 6log₆(c) − 30log₆(b)

• log(x) + log(z) + 4log(y)
• 3log(x) − log(z) − 4log(y)
• 3log(x) + log(z) + 4log(y)
• log(x) − 4log(z) − 3log(y)

• log₈(a²/cb³)
• log₈(ca²/b³)
• log₈(a²cb³)
• log(a² − c − b³) 

• log₅(x²z²y¹⁰)
• log₅(z²y²x¹⁰)
• log(zy²x¹⁰)
• log₅(z² + y² + x¹⁰)

• 24log(u) - log(v)
• 24log(u) + 6log(v)
• 4log(u) + 6log(v)
• 4log(u) - 6log(v)

• 60 log(ab)
• 6log(a) + log(b)
• log(a) - 30 log(b)
• 6log(a) + 30 log(b)

• 2ln(xyz)
• ln(x) + ln(y) + ln(z)
• ln(x) - ln(y) - 2ln(z)
• ln(x) + ln(y) + 2ln(z)