What is log_{7}(4)*log_{2}(5)+log_{7}(49/25) ?

The solution to log_{7}(4)*log_{2}(5)+log_{7}(49/25) is 2

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simplify log_{7}(4)*log_{2}(5)+log_{7}(49/25)

simplify

lo g_{7} (4) \cdot lo g_{2} (5) + lo g_{7} (\frac{49}{25})

2

Solution steps

lo g_{7} (4) lo g_{2} (5) + lo g_{7} (\frac{49}{25})

Apply log rule:

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

lo g_{7} (4) lo g_{2} (5) = lo g_{7} (4^{l o g_{2} (5)})

= lo g_{7} (4^{l o g_{2} (5)}) + lo g_{7} (\frac{49}{25})

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{7} (4^{l o g_{2} (5)}) + lo g_{7} (\frac{49}{25}) = lo g_{7} (4^{l o g_{2} (5)} \cdot \frac{49}{25})

= lo g_{7} (4^{l o g_{2} (5)} \cdot \frac{49}{25})

Simplify

4^{l o g_{2} (5)} \cdot \frac{49}{25} : 49

= lo g_{7} (49)

Factor the number:

49 = 7^{2}

= lo g_{7} (7^{2})

Apply log rule:

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

= 2

\frac{1}{3} lo g_{3} (2)

\frac{\partial}{\partial x} (x^{2} y) + ln (x y^{2})

ln (\frac{( 1 + e ^{x} )}{( 1 - e ^{x} )})

lo g_{b} (\frac{a ^{2} b ^{3}}{c ^{4} m})

4 ln (x) + 4 ln (y)

What is log_{7}(4)*log_{2}(5)+log_{7}(49/25) ?
The solution to log_{7}(4)*log_{2}(5)+log_{7}(49/25) is 2