What is the answer to 4*10^{2x}+1=21 ?

The answer to 4*10^{2x}+1=21 is x=(ln(5))/(2ln(10))

Solve for x: 4*10^{2x}+1=21

The solution is x=(ln(5))/(2ln(10))

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4 \cdot 1 0^{2 x} + 1 = 21

x = \frac{ln ( 5 )}{2 ln ( 10 )}

Decimal Notation

x = 0.34948 \dots

Solution steps

4 \cdot 1 0^{2 x} + 1 = 21

Move

1

to the right side

4 \cdot 1 0^{2 x} = 20

Divide both sides by

4

1 0^{2 x} = 5

Apply exponent rules

2 x ln (10) = ln (5)

Solve

2 x ln (10) = ln (5) : x = \frac{ln ( 5 )}{2 ln ( 10 )}

x = \frac{ln ( 5 )}{2 ln ( 10 )}

x, e^{l n (x)} = e^{y + c}

2 (4^{2 x + 1}) = 128

3^{x} = \frac{1}{4}

2^{- 3 x + 1} = \frac{1}{16}

e^{7 x} = 23

What is the answer to 4*10^{2x}+1=21 ?
The answer to 4*10^{2x}+1=21 is x=(ln(5))/(2ln(10))
Solve for x: 4*10^{2x}+1=21
The solution is x=(ln(5))/(2ln(10))