what is the solution to $\log_{5}(10x-1) = \log_{5}(9x+7)$?

$x = \frac{6}{19}$

$x = \frac{8}{19}$

$x = 7$

$x = 8$

Question

what is the solution to $\log_{5}(10x-1) = \log_{5}(9x+7)$?

$x = \frac{6}{19}$

$x = \frac{8}{19}$

$x = 7$

$x = 8$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Logarithmic Equations", "One-to-One Property" ], "new_concepts": [], "current_concepts": [ "Logarithmic Equations", "One-to-One Property" ] } ## Equate the arguments using the one-to-one property $$ \begin{aligned} \log_5(10x - 1) &= \log_5(9x + 7) \ 10x - 1 &= 9x + 7 \end{aligned} $$ ## Solve for x $$ \begin{aligned} 10x - 9x &= 7 + 1 \ x &= 8 \end{aligned} $$ ## Verify the solution in the original domain $$ \begin{aligned} 10(8) - 1 &= 79 > 0 \ 9(8) + 7 &= 79 > 0 \end{aligned} $$

(A) $x = \frac{6}{19}$

(B) $x = \frac{8}{19}$

(C) $x = 7$

(D) $x = 8$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Logarithmic Equations" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Equate the arguments using the one-to-one property

Solve for x

Verify the solution in the original domain

Answer: