solve for the variable.\n-7 - 10 log 6r = -27\nanswer:

Answer:

$r = \dfrac{5}{3}$

Explanation:

Step1: Isolate the logarithmic term

$$ \begin{align*} -7-10\log6r&=-27\ -10\log6r&=-27 + 7\ -10\log6r&=-20 \end{align*} $$

Step2: Solve for the logarithm

Divide both sides by $- 10$: $$\log6r = 2$$

Step3: Convert to exponential form

Using the definition of logarithm ($\log_{10}a=b\Rightarrow a = 10^{b}$), we have: $$6r=10^{2}$$ $$6r = 100$$

Step4: Solve for $r$

Divide both sides by $6$: $$r=\dfrac{100}{6}=\dfrac{50}{3}$$