What is 2log_{10}(a)+5log_{10}(b) ?

The solution to 2log_{10}(a)+5log_{10}(b) is log_{10}(a^2b^5)

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simplify 2log_{10}(a)+5log_{10}(b)

simplify

2 lo g_{10} (a) + 5 lo g_{10} (b)

lo g_{10} (a^{2} b^{5})

Solution steps

2 lo g_{10} (a) + 5 lo g_{10} (b)

Apply log rule:

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

2 lo g_{10} (a) = lo g_{10} (a^{2})

= lo g_{10} (a^{2}) + 5 lo g_{10} (b)

Apply log rule:

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

5 lo g_{10} (b) = lo g_{10} (b^{5})

= lo g_{10} (a^{2}) + lo g_{10} (b^{5})

Apply log rule:

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

lo g_{10} (a^{2}) + lo g_{10} (b^{5}) = lo g_{10} (a^{2} b^{5})

= lo g_{10} (a^{2} b^{5})

ln (7) - ln (2)

ln (x) + ln (5)

lo g_{10} (\frac{x}{10})

lo g_{10} (4) + 3 lo g_{10} (x) + lo g_{10} (y)

8 ln (x) - \frac{1}{4} ln (y)

What is 2log_{10}(a)+5log_{10}(b) ?
The solution to 2log_{10}(a)+5log_{10}(b) is log_{10}(a^2b^5)