What is 10log_{10}(5.2x10^6) ?

The solution to 10log_{10}(5.2x10^6) is 10log_{10}(52)+10log_{10}(x)+50

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simplify 10log_{10}(5.2x10^6)

simplify

10 lo g_{10} (5.2 x 1 0^{6})

10 lo g_{10} (52) + 10 lo g_{10} (x) + 50

Solution steps

10 lo g_{10} (5.2 x \cdot 1 0^{6})

Simplify

lo g_{10} (5.2 x \cdot 1 0^{6}) : lo g_{10} (52 x) + 5

= 10 (lo g_{10} (52 x) + 5)

Simplify

10 (lo g_{10} (52 x) + 5) : 10 lo g_{10} (52) + 10 lo g_{10} (x) + 50

= 10 lo g_{10} (52) + 10 lo g_{10} (x) + 50

Apply log rule:

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

10 lo g_{10} (52) = lo g_{10} (5 2^{10})

= lo g_{10} (5 2^{10}) + 10 lo g_{10} (x) + 50

Apply log rule:

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

10 lo g_{10} (x) = lo g_{10} (x^{10})

= lo g_{10} (5 2^{10}) + lo g_{10} (x^{10}) + 50

Apply log rule:

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

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

= lo g_{10} (5 2^{10} x^{10}) + 50

Simplify

lo g_{10} (5 2^{10} x^{10}) : 10 lo g_{10} (52) + 10 lo g_{10} (x)

= 10 lo g_{10} (52) + 10 lo g_{10} (x) + 50

lo g_{b} (y^{4} x)

lo g_{b} (y^{4} z)

lo g_{10} (\frac{x ^{2} y ^{3}}{100})

- \frac{4}{7} \cdot lo g_{2} (\frac{4}{7}) - \frac{3}{7} \cdot lo g_{2} (\frac{3}{7})

lo g_{5} (\frac{( \frac{5 x}{x + 2} )}{x + 6} \cdot x)

What is 10log_{10}(5.2x10^6) ?
The solution to 10log_{10}(5.2x10^6) is 10log_{10}(52)+10log_{10}(x)+50