1 Answer

Tidhar Klein Orbach · Answer 1 · 2023-04-14T06:19:59+0000

We want to rewrite the following logarithm

$\log_b√(6x)$

To rewrite this logarithm, first let's rewrite the argument of the logarithm. Using the following property

$√(a)=a^{(1)/(2)}$

We can rewrite our expression as

$\operatorname{\log}_b√(6x)=\operatorname{\log}_b6x^{(1)/(2)}$

Using the following property

$\log_nx^m=m\log_nx$

We can rewrite our expression as

$\operatorname{\log}_b6x^{(1)/(2)}=(1)/(2)\operatorname{\log}_b6x$

and finally, using the logarithm property of a product

$\log_n(x\cdot y)=\log_nx+\log_ny$

We can rewrite our expression as

$\begin{gathered} (1)/(2)\operatorname{\log}_b6x=(1)/(2)\operatorname{\log}_b(6\cdot x) \\ =(1)/(2)(\log_b6+\log_bx) \end{gathered}$

and this is the final form of our expression.

$\operatorname{\log}_b√(6x)=(1)/(2)(\log_b6+\log_bx)$

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