What is the answer to A(x)=500(1.03)^x ?

The answer to A(x)=500(1.03)^x is x=-(\W(-(500ln(1.03))/A))/(ln(1.03))

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A(x)=500(1.03)^x

A (x) = 500 (1.03)^{x}

x = - \frac{W ( - \frac{500 l n ( 1.03 )}{A} )}{ln ( 1.03 )}

Solution steps

A (x) = 500 (1.03)^{x}

Prepare

A (x) = 500 (1.03)^{x}

for Lambert form:

A x e^{- l n (1.03) x} = 500

Rewrite the equation with

- x ln (1.03) = u

and

x = - \frac{u}{ln ( 1.03 )}

A (- \frac{u}{ln ( 1.03 )}) e^{u} = 500

Rewrite

A (- \frac{u}{ln ( 1.03 )}) e^{u} = 500

in Lambert form:

e^{u} u = - \frac{500 ln ( 1.03 )}{A}

Solve

e^{u} u = - \frac{500 ln ( 1.03 )}{A} : u = W (- \frac{500 ln ( 1.03 )}{A})

u = W (- \frac{500 ln ( 1.03 )}{A})

Substitute back

u = - x ln (1.03),

solve for

x

Solve

- x ln (1.03) = W (- \frac{500 ln ( 1.03 )}{A}) : x = - \frac{W ( - \frac{500 l n ( 1.03 )}{A} )}{ln ( 1.03 )}

x = - \frac{W ( - \frac{500 l n ( 1.03 )}{A} )}{ln ( 1.03 )}

4 9^{x + 3} = 7^{x^{2} - 3 x + 8}

8^{x} = 360000000

3^{x + 1} + 3^{x - 1} = 90

7^{q} = 49

2000 = 1000 e^{0.09 x}

What is the answer to A(x)=500(1.03)^x ?
The answer to A(x)=500(1.03)^x is x=-(\W(-(500ln(1.03))/A))/(ln(1.03))