How do you write as a single logarithm $\frac{1}{2} {log}_{b} 3 + \frac{1}{2} {log}_{b} x - 3 {log}_{b} Z$ $1/2 Log _b3 +1/2 Log_bx - 3 Log_b Z$ ?

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Answer 1 · 2018-03-15T12:17:21

${log}_{b} (\frac{\sqrt{3 x}}{Z^{3}})$ $log_b(sqrt(3x)/Z^3)$

Since $x log y = {log y}^{x}$ $xlogy=logy^x$ , we can write:

${log}_{b} \sqrt{3} + {log}_{b} \sqrt{x} - {log}_{b} Z^{3}$ $log_bsqrt(3)+log_bsqrt(x)-log_bZ^3$

Since $log a + log b = log (a b)$ $loga+logb=log(ab)$ , we write:

${log}_{b} \sqrt{3 x} - {log}_{b} Z^{3}$ $log_bsqrt(3x)-log_bZ^3$

Since $log a - log b = log (\frac{a}{b})$ $loga-logb=log(a/b)$ , we can write:

${log}_{b} (\frac{\sqrt{3 x}}{Z^{3}})$ $log_b(sqrt(3x)/Z^3)$

How do you write as a single logarithm 12logb3+12logbx−3logbZ1/2 Log _b3 +1/2 Log_bx - 3 Log_b Z?