Question Type 3: Using standard logarithms to rewrite expressions Exercises

Express $3 + \log_{10}(x)$ as a single base-$10$ logarithm.

Rewrite $\log_{5}(1) + 3$ as a single base-$5$ logarithm.

Simplify $\log_{7}(49) + 1$ into a single logarithm (base 7).

Simplify the expression $2 - \log_{3}(9)$ using logarithm properties.

Simplify $-1 + \log_{2}(4)$ as a single logarithm (base 2).

Simplify the expression $3 + \log_{2}(5)$ as a single logarithm.

Combine $4 + \log_{4}(7)$ into a single logarithm (base 4).

Simplify $\tfrac{1}{2} + \log_{10}(4)$ as a single base-$10$ logarithm.

Simplify the expression $1 - \log_{2}(8)$ as a single base-$2$ logarithm.

Express $5 + \log_{5}(2)$ as a single logarithm with base 5.

Combine $2 + \log_{3}(5)$ into a single logarithm (base 3).

Express $3 + \log_{x}(y)$ as a single logarithm with base $x$.