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2 years ago

What is the solution to the equation below? riund your answer to two decimal places. (24) log(3x) = 60

Mathematics

1 answer:

Amanda [17]2 years ago

8 0

The answer is: " x = 105.41 " .

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Explanation:

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Given: " 24 log (3x) = 60 " ; Solve for "x" .

The default is to assume "base 10" for the "logarithm".

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Start by dividing each side of the equation by "24" ;

→ [ 24 log(3x) ] / 24 = 60 / 24 ;

to get:

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log (3x) = 2.5 ;

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Rewrite as: log₁₀ (3x) = 2.5 ;

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Using the property of logarithms:

⇔ 10⁽²·⁵⁾ = 3x ;

↔ 3x = 10⁽²·⁵⁾ ;

→ 10^ (2.5) = 316.2277660168379332 ;

→ 3x = 316.227766016837933 ;

Divide each side of the equation by "3" ;

to isolate "x" on one side of the equation;

and to solve for "x" ;

→ 3x / 3 = 316.2277660168379332 / 3 ;

to get:

→ x = 105.4092553389459777333 ;

→ round to 2 (two) decimal places;

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→ " x = 105.41 " .

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Hope this helps!

Best wishes to you!

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