Combining Logarithms

Rewrite log_pt = m in exponential form.

• p^t = m
• t^m = p
• m^t = p
• p^m = t

Condense into a single logarithm. 6 log x

• A

• B

• C

• D

Condense into a single logarithm. 10 log₂x - 5 log₂y

• A

• B

• C

• D

Condense log x + log y + 3 log z

• log xyz³

• log (xy/z³)

• logx+logy+logz³

• logx³y³z³

Condense 6log₈x-3log₈y

• log₈(x⁶)/log₈(y³)

• log₈(x⁶/y³)

• log₈(x/y³)

• log₈(x⁶y³)

Expand log₈(ab)

• log₈a/2

• log₈(a)+log₈(b)

• blog₈(a)

• log₈(a)-log₈(b)

Write the expression as a single logarithm. Then simplify if possible.

log₅ 3 + log₅ x+ log₅ 9

• log₅ 12x

• log₅ 6x

• log₅ 27x

• log₅ 39x

• log m^2 + log q^4 - log 3

• 2 log m + 4 log q - log 3

• 2 log m - 4 log q + log 3

• log m x log 2 + log q x log 4 - log 3

Separate; write as multiple logs: log 2x^3

• log 2 + 3 log x

• 3 log 2x

• (log 2)(3 log x)

• 2 log x^3

Rewrite as a single log: 

4 log g - 2 log h

• log (g^4 - h^2)

• log (2gh)