What is the answer to 0.4=1.05^{2x+5}-1 ?

The answer to 0.4=1.05^{2x+5}-1 is x=(ln(1.4)-5ln(1.05))/(2ln(1.05))

Solve for x: 0.4=1.05^{2x+5}-1

The solution is x=(ln(1.4)-5ln(1.05))/(2ln(1.05))

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0.4 = 1.0 5^{2 x + 5} - 1

x = \frac{ln ( 1.4 ) - 5 ln ( 1.05 )}{2 ln ( 1.05 )}

Decimal Notation

x = 0.94815 \dots

Solution steps

0.4 = 1.0 5^{2 x + 5} - 1

Switch sides

1.0 5^{2 x + 5} - 1 = 0.4

Move

1

to the right side

1.0 5^{2 x + 5} = 1.4

Apply exponent rules

(2 x + 5) ln (1.05) = ln (1.4)

Solve

(2 x + 5) ln (1.05) = ln (1.4) : x = \frac{ln ( 1.4 ) - 5 ln ( 1.05 )}{2 ln ( 1.05 )}

x = \frac{ln ( 1.4 ) - 5 ln ( 1.05 )}{2 ln ( 1.05 )}

0 = x (2 - x) e^{(- x + 4)}

4 ∣ 5^{x} - 1 ∣ = 5^{x}

3^{2 x - 2} = 9

\frac{1}{49} = 34 3^{x}

3^{2 x} - 1 = 15

What is the answer to 0.4=1.05^{2x+5}-1 ?
The answer to 0.4=1.05^{2x+5}-1 is x=(ln(1.4)-5ln(1.05))/(2ln(1.05))
Solve for x: 0.4=1.05^{2x+5}-1
The solution is x=(ln(1.4)-5ln(1.05))/(2ln(1.05))