What is 1/2 log_{b}(57)+1/2 log_{b}(74) ?

The solution to 1/2 log_{b}(57)+1/2 log_{b}(74) is 1/2 log_{b}(4218)

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simplify 1/2 log_{b}(57)+1/2 log_{b}(74)

simplify

\frac{1}{2} lo g_{b} (57) + \frac{1}{2} lo g_{b} (74)

\frac{1}{2} lo g_{b} (4218)

Solution steps

\frac{1}{2} lo g_{b} (57) + \frac{1}{2} lo g_{b} (74)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} lo g_{b} (57) = lo g_{b} (5 7^{\frac{1}{2}})

= lo g_{b} (5 7^{\frac{1}{2}}) + \frac{1}{2} lo g_{b} (74)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} lo g_{b} (74) = lo g_{b} (7 4^{\frac{1}{2}})

= lo g_{b} (5 7^{\frac{1}{2}}) + lo g_{b} (7 4^{\frac{1}{2}})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{b} (5 7^{\frac{1}{2}}) + lo g_{b} (7 4^{\frac{1}{2}}) = lo g_{b} (5 7^{\frac{1}{2}} \cdot 7 4^{\frac{1}{2}})

= lo g_{b} (5 7^{\frac{1}{2}} \cdot 7 4^{\frac{1}{2}})

5 7^{\frac{1}{2}} \cdot 7 4^{\frac{1}{2}} = 4218

= lo g_{b} (4218)

Rewrite as

= lo g_{b} (421 8^{\frac{1}{2}})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= \frac{1}{2} lo g_{b} (4218)

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What is 1/2 log_{b}(57)+1/2 log_{b}(74) ?
The solution to 1/2 log_{b}(57)+1/2 log_{b}(74) is 1/2 log_{b}(4218)