Finite Math Examples

Solve for z (10e^(3z-7))/10=5/10
Step 1
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
Step 2
Divide each term in by and simplify.
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Step 2.1
Divide each term in by .
Step 2.2
Simplify the left side.
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Step 2.2.1
Cancel the common factor of .
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Step 2.2.1.1
Cancel the common factor.
Step 2.2.1.2
Divide by .
Step 2.3
Simplify the right side.
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Step 2.3.1
Cancel the common factor of and .
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Step 2.3.1.1
Factor out of .
Step 2.3.1.2
Cancel the common factors.
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Step 2.3.1.2.1
Factor out of .
Step 2.3.1.2.2
Cancel the common factor.
Step 2.3.1.2.3
Rewrite the expression.
Step 3
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 4
Expand the left side.
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Step 4.1
Expand by moving outside the logarithm.
Step 4.2
The natural logarithm of is .
Step 4.3
Multiply by .
Step 5
Add to both sides of the equation.
Step 6
Divide each term in by and simplify.
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Step 6.1
Divide each term in by .
Step 6.2
Simplify the left side.
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Step 6.2.1
Cancel the common factor of .
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Step 6.2.1.1
Cancel the common factor.
Step 6.2.1.2
Divide by .
Step 7
The result can be shown in multiple forms.
Exact Form:
Decimal Form: