What is 1/2 log_{10}(x)-log_{10}(2)-7log_{10}(m) ?

The solution to 1/2 log_{10}(x)-log_{10}(2)-7log_{10}(m) is log_{10}((sqrt(x))/(2m^7))

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simplify 1/2 log_{10}(x)-log_{10}(2)-7log_{10}(m)

simplify

\frac{1}{2} lo g_{10} (x) - lo g_{10} (2) - 7 lo g_{10} (m)

lo g_{10} (\frac{x}{2 m ^{7}})

Solution steps

\frac{1}{2} lo g_{10} (x) - lo g_{10} (2) - 7 lo g_{10} (m)

\frac{1}{2} lo g_{10} (x) = lo g_{10} (x^{\frac{1}{2}})

- 7 lo g_{10} (m) = - lo g_{10} (m^{7})

= lo g_{10} (x^{\frac{1}{2}}) - lo g_{10} (2) - lo g_{10} (m^{7})

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (x^{\frac{1}{2}}) - lo g_{10} (2) = lo g_{10} (\frac{x ^{\frac{1}{2}}}{2})

= lo g_{10} (\frac{x ^{\frac{1}{2}}}{2}) - lo g_{10} (m^{7})

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (\frac{x ^{\frac{1}{2}}}{2}) - lo g_{10} (m^{7}) = lo g_{10} \frac{\frac{x ^{\frac{1}{2}}}{2}}{m ^{7}}

= lo g_{10} \frac{\frac{x ^{\frac{1}{2}}}{2}}{m ^{7}}

Simplify

\frac{\frac{x ^{\frac{1}{2}}}{2}}{m ^{7}} : \frac{x ^{\frac{1}{2}}}{2 m ^{7}}

= lo g_{10} (\frac{x ^{\frac{1}{2}}}{2 m ^{7}})

Apply exponent rule:

a^{\frac{1}{2}} = a

x^{\frac{1}{2}} = x

= lo g_{10} (\frac{x}{2 m ^{7}})

\frac{2 ln ( 2 )}{ln ( 2 ) - ln ( 3 )}

lo g_{10} (2 x + 9) - lo g_{10} (x)

lo g_{\frac{1}{4}} (16 z (x^{3} - 27))

\frac{1}{2} ln 3 + e^{8} - ln (2)

lo g_{z} (\frac{2 x}{3})

What is 1/2 log_{10}(x)-log_{10}(2)-7log_{10}(m) ?
The solution to 1/2 log_{10}(x)-log_{10}(2)-7log_{10}(m) is log_{10}((sqrt(x))/(2m^7))