Question

exprese como un solo logaritmo .. por favor ... help me

Answer 1

$\frac{1}{2}\log _5\left(49\right)-\frac{1}{3}\log _5\left(8\right)+13\log _5\left(1\right)$

Logaritmo de 1 = 0

$13\log _5\left(1\right) = 0$

$\log _a\left(x^b\right)=b\cdot \log _a\left(x\right)$

$\frac{1}{2}\log _5\left(49\right) = \frac{1}{2}2\log _5\left(7\right)$

$\frac{1}{2}\log _5\left(49\right) =\log _5\left(7\right)$

$\frac{1}{3}\log _5\left(8\right) = \frac{1}{3}\log _5\left(2^3\right)$

$3 \frac{1}{3}\log _5\left(2\right) = \log _5\left(2\right)$

Ahora:
$\log _5\left(7\right)-\log _5\left(2\right)$

Aplicamos:

$\log _c\left(a\right)-\log _c\left(b\right)=\log _c\left(\frac{a}{b}\right)$

= $\log _5\left(\frac{7}{2}\right)$ (Expresion Final)