Laws of Logarithms

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)

Evaluate log_b(1)

• 0
• 1
• -1
• b

Evaluate log_b(b)

• -1
• 0
• 1
• b

Evaluate log_b(b^x)

• 1
• 0
• x
• b

log_bx=y iff _______

• b^y=x
• log_by=x
• b^x=y
• log_xb=y

Tags

CCSS.HSF.BF.B.5

Condense

• A
• B
• C
• D

Condense

• A
• B
• C
• D

Write the expression as a single logarithm.   Then simplify if possible.
log₅3 + log₅6 + log₅9

• log₅69
• log₅56
• log₅162
• log₅98