# Solve for a 7^(a+2)+4*7^(a-1)=35

Rewrite as .
Rewrite as .
Substitute for .
Solve for .
Simplify .
Simplify each term.
Raise to the power of .
Rewrite the expression using the negative exponent rule .
Combine and .
Combine and .
To write as a fraction with a common denominator, multiply by .
Simplify terms.
Combine and .
Combine the numerators over the common denominator.
Simplify each term.
Simplify the numerator.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Multiply by .
Move to the left of .
Add to both sides of the equation.
Multiply both sides of the equation by .
Simplify both sides of the equation.
Simplify .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply .
Combine and .
Multiply by .
Substitute for in .
Solve .
Rewrite the equation as .
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Expand by moving outside the logarithm.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Solve for a 7^(a+2)+4*7^(a-1)=35

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