The answer is: " x = 105.41 " .
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Step-by-step 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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