What is 5*log_{10}(a)+1/2*log_{10}(b)-4*log_{10}(c) ?

The solution to 5*log_{10}(a)+1/2*log_{10}(b)-4*log_{10}(c) is log_{10}((a^5b^{1/2})/(c^4))

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simplify 5log_{10}(a)+1/2log_{10}(b)-4*log_{10}(c)

simplify

5 \cdot lo g_{10} (a) + \frac{1}{2} \cdot lo g_{10} (b) - 4 \cdot lo g_{10} (c)

lo g_{10} (\frac{a ^{5} b ^{\frac{1}{2}}}{c ^{4}})

Solution steps

5 lo g_{10} (a) + \frac{1}{2} lo g_{10} (b) - 4 lo g_{10} (c)

Apply log rule:

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

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

= lo g_{10} (a^{5}) + \frac{1}{2} lo g_{10} (b) - 4 lo g_{10} (c)

Apply log rule:

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

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

= lo g_{10} (a^{5}) + lo g_{10} (b^{\frac{1}{2}}) - 4 lo g_{10} (c)

Apply log rule:

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

lo g_{10} (a^{5}) + lo g_{10} (b^{\frac{1}{2}}) = lo g_{10} (a^{5} b^{\frac{1}{2}})

= lo g_{10} (a^{5} b^{\frac{1}{2}}) - 4 lo g_{10} (c)

Apply log rule:

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

4 lo g_{10} (c) = lo g_{10} (c^{4})

= lo g_{10} (a^{5} b^{\frac{1}{2}}) - lo g_{10} (c^{4})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{10} (a^{5} b^{\frac{1}{2}}) - lo g_{10} (c^{4}) = lo g_{10} (\frac{a ^{5} b ^{\frac{1}{2}}}{c ^{4}})

= lo g_{10} (\frac{a ^{5} b ^{\frac{1}{2}}}{c ^{4}})

\frac{ln ( x + h ) - ln ( x )}{h}

lo g_{10} (m) + lo g_{10} (n)

lo g_{10} (\frac{x}{5})

ln (14) - ln (7)

lo g_{4} (8) + 2 lo g_{4} (7)

What is 5*log_{10}(a)+1/2*log_{10}(b)-4*log_{10}(c) ?
The solution to 5*log_{10}(a)+1/2*log_{10}(b)-4*log_{10}(c) is log_{10}((a^5b^{1/2})/(c^4))