Use the properties of logarithms to rewrite the following ex

Use the properties of logarithms to rewrite the following expression as a sum or difference of logarithms each of which is the logarithm of an integer or a variable. Assume all variables represent positive real numbers. log_10(5x/11) log_10(5x/11) =

Solution

log₁₀[5x/11]

log A - log B = log(A/B)

so, log₁₀[5x/11] = log₁₀ (5x) - log₁₀ (11)

also, logA + log B = log (AB)

therefore, log₁₀[5x/11] = [log₁₀ (5) + log₁₀ + log₁₀ x - log₁₀ (11).