Question
Solve the equation
Solve for m
Solve for n
m=8log2(3)−2+n
Evaluate
272×163322×32=2n2m
Simplify
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Evaluate
272×163322×32
Divide the terms
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Evaluate
163322
Rewrite the expression
163210
Rewrite the expression
212210
Use the product rule aman=an−m to simplify the expression
212−101
Subtract the terms
221
272×221×32
Transform the expression
36×221×32
Multiply the terms with the same base by adding their exponents
36+2×221
Add the numbers
38×221
Multiply the numbers
2238
2238=2n2m
Simplify
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Evaluate
2n2m
Dividing by an is the same as multiplying by a−n
2m×2−n
Multiply the terms with the same base by adding their exponents
2m−n
2238=2m−n
Swap the sides of the equation
2m−n=2238
Take the logarithm of both sides
log2(2m−n)=log2(2238)
Evaluate the logarithm
m−n=log2(2238)
Move the expression to the right-hand side and change its sign
m=log2(2238)+n
Solution
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Evaluate
log2(2238)
Use loga(yx)=loga(x)−loga(y) to transform the expression
log2(38)−log2(22)
Use logabn=nlogab to simplify the expression
8log2(3)−log2(22)
Use logaan=n to simplify the expression
8log2(3)−2
m=8log2(3)−2+n
Show Solution
