Help me solve this equation: If 4/3^m+2 = 9/16, find m.

All QuestionsCategory: Secondary SchoolHelp me solve this equation: If 4/3^m+2 = 9/16, find m.
Mary Efue asked 9 months ago

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1 Answers
User AvatarStopLearn Team Staff answered 9 months ago

To solve the equation 43m+2=9163m+24=169 for mm, you can follow these steps:
Step 1: Cross-multiply to eliminate the fractions:
4⋅16=9⋅3m+2416=93m+2
Step 2: Simplify both sides of the equation:
64=9⋅3m+264=93m+2
Step 3: Divide both sides by 9 to isolate 3m+23m+2:
649=3m+2964=3m+2
Step 4: Take the logarithm (base 3) of both sides to solve for m+2m+2:
m+2=log⁡3(649)m+2=log3(964)
Step 5: Now, subtract 2 from both sides to find mm:
m=log⁡3(649)−2m=log3(964)2
To compute the value of mm, you can use a calculator or software with logarithmic functions. The value of mm should be approximately:
m≈log⁡3(649)−2mlog3(964)2

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