A single expression for the logarithmic expression log⁡10x5−log⁡5x

Question

Neelam Wainwright · Accepted Answer

Formula used:
Quotient rule of logarithm is given by

\log_{a} m - \log_{a} n = \log_{a} (\frac{m}{n})

Quotient rule of exponent is given by

\frac{x^{a}}{x^{b}} = x^{a - b}

Calculation:
We have been given the expression

\log 10 x^{5} - \log 5 x

and we need to write it in single logarithmic expression. For this we will do below steps:

\log 10 x^{5} - \log 5 x

Given expression

= \log (\frac{10 x^{5}}{5 x})

Quotient rule:

\log_{a} m - \log_{a} n = \log_{a} (\frac{m}{n})

= \log (2 x^{4})

Exponent property

\frac{x^{a}}{x^{b}} = x^{a - b}

Thus, the required single logarithmic expression is given by

\log (2 x^{4})

Conclusion:
Using the properties of logarithms, the single logarithmic expression is given by

\log (2 x^{4})

A single expression for the logarithmic expression \log 10x^{5}-\log 5x