What is the answer to 5=a\times b^{-(x-c)}+d ?

The answer to 5=a\times b^{-(x-c)}+d is x=-(ln((5-d)/a))/(ln(b))+c

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5=a\times b^{-(x-c)}+d

5 = a \cdot b^{- (x - c)} + d

x = - \frac{ln ( \frac{5 - d}{a} )}{ln ( b )} + c

Solution steps

5 = a b^{- (x - c)} + d

Switch sides

a b^{- (x - c)} + d = 5

Move

d

to the right side

a b^{- (x - c)} = 5 - d

Divide both sides by

a

b^{- (x - c)} = \frac{5 - d}{a}

Apply exponent rules

- (x - c) ln (b) = ln (\frac{5 - d}{a})

Solve

- (x - c) ln (b) = ln (\frac{5 - d}{a}) : x = - \frac{ln ( \frac{5 - d}{a} )}{ln ( b )} + c

x = - \frac{ln ( \frac{5 - d}{a} )}{ln ( b )} + c

1 6^{3 x - 2} = 3 2^{x + 4}

9^{x} - 2 \times 3^{x + 2} + 81 = 0

8^{x} = 1024

e^{x} - e^{- 3} = 0

e^{2 x} - 12 = 4 e^{x}

What is the answer to 5=a\times b^{-(x-c)}+d ?
The answer to 5=a\times b^{-(x-c)}+d is x=-(ln((5-d)/a))/(ln(b))+c