dolovatgyp

2022-04-26

Simplify expression using the properties of logarithms

$\mathrm{log}}_{53}k+{\mathrm{log}}_{57}{k}^{3$

Isla Preston

Beginner2022-04-27Added 12 answers

According to the product rule of logarithm, ${\mathrm{log}}_{a}x+{\mathrm{log}}_{a}y={\mathrm{log}}_{a}xy$ .

So, use the product rule of logarithm to combine the logarithm terms.

${\mathrm{log}}_{53}k+{\mathrm{log}}_{57}{k}^{3}={\mathrm{log}}_{5}(3k\cdot 7{k}^{3})$

Now, simplify the expression as follows:

$\mathrm{log}}_{5}(3k\cdot 7{k}^{3})={\mathrm{log}}_{521}{k}^{4$

Therefore,$\mathrm{log}}_{53}k+{\mathrm{log}}_{57}{k}^{3}={\mathrm{log}}_{521}{k}^{4$ .

So, use the product rule of logarithm to combine the logarithm terms.

Now, simplify the expression as follows:

Therefore,

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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