What is 2log_{b}(a)+3log_{b}(c^2)-4log_{b}(d) ?

The solution to 2log_{b}(a)+3log_{b}(c^2)-4log_{b}(d) is log_{b}((a^2c^6)/(d^4))

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simplify 2log_{b}(a)+3log_{b}(c^2)-4log_{b}(d)

simplify

2 lo g_{b} (a) + 3 lo g_{b} (c^{2}) - 4 lo g_{b} (d)

lo g_{b} (\frac{a ^{2} c ^{6}}{d ^{4}})

Solution steps

2 lo g_{b} (a) + 3 lo g_{b} (c^{2}) - 4 lo g_{b} (d)

Apply log rule:

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

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

= lo g_{b} (a^{2}) + 3 lo g_{b} (c^{2}) - 4 lo g_{b} (d)

Apply log rule:

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

3 lo g_{b} (c^{2}) = lo g_{b} ((c^{2})^{3})

= lo g_{b} (a^{2}) + lo g_{b} ((c^{2})^{3}) - 4 lo g_{b} (d)

Apply log rule:

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

lo g_{b} (a^{2}) + lo g_{b} ((c^{2})^{3}) = lo g_{b} (a^{2} (c^{2})^{3})

= lo g_{b} (a^{2} (c^{2})^{3}) - 4 lo g_{b} (d)

(c^{2})^{3} = c^{6}

= lo g_{b} (a^{2} c^{6}) - 4 lo g_{b} (d)

Apply log rule:

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

4 lo g_{b} (d) = lo g_{b} (d^{4})

= lo g_{b} (a^{2} c^{6}) - lo g_{b} (d^{4})

Apply log rule:

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

lo g_{b} (a^{2} c^{6}) - lo g_{b} (d^{4}) = lo g_{b} (\frac{a ^{2} c ^{6}}{d ^{4}})

= lo g_{b} (\frac{a ^{2} c ^{6}}{d ^{4}})

lo g_{4} (a^{3} b^{3} \cdot c)

- 0.7 lo g_{2} (0.7) - 0.3 lo g_{2} (0.3)

lo g_{7} (x + 1) - lo g_{7} (\frac{1}{x + 1})

ln (3 ab \cdot 5 c)

What is 2log_{b}(a)+3log_{b}(c^2)-4log_{b}(d) ?
The solution to 2log_{b}(a)+3log_{b}(c^2)-4log_{b}(d) is log_{b}((a^2c^6)/(d^4))