Algebra Examples

Solve for w 0.75*10^(w/3)=30
0.7510w3=300.7510w3=30
Step 1
Divide each term in 0.7510w3=300.7510w3=30 by 0.750.75 and simplify.
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Step 1.1
Divide each term in 0.7510w3=300.7510w3=30 by 0.750.75.
0.7510w30.75=300.750.7510w30.75=300.75
Step 1.2
Simplify the left side.
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Step 1.2.1
Cancel the common factor of 0.750.75.
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Step 1.2.1.1
Cancel the common factor.
0.7510w30.75=300.75
Step 1.2.1.2
Divide 10w3 by 1.
10w3=300.75
10w3=300.75
10w3=300.75
Step 1.3
Simplify the right side.
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Step 1.3.1
Divide 30 by 0.75.
10w3=40
10w3=40
10w3=40
Step 2
Take the base 10 logarithm of both sides of the equation to remove the variable from the exponent.
log(10w3)=log(40)
Step 3
Expand the left side.
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Step 3.1
Expand log(10w3) by moving w3 outside the logarithm.
w3log(10)=log(40)
Step 3.2
Logarithm base 10 of 10 is 1.
w31=log(40)
Step 3.3
Multiply w3 by 1.
w3=log(40)
w3=log(40)
Step 4
Multiply both sides of the equation by 3.
3w3=3log(40)
Step 5
Simplify the left side.
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Step 5.1
Cancel the common factor of 3.
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Step 5.1.1
Cancel the common factor.
3w3=3log(40)
Step 5.1.2
Rewrite the expression.
w=3log(40)
w=3log(40)
w=3log(40)
Step 6
The result can be shown in multiple forms.
Exact Form:
w=3log(40)
Decimal Form:
w=4.80617997
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