What is the answer to 2^x*0.2^5=2^{10} ?

The answer to 2^x*0.2^5=2^{10} is x=(ln(\frac{1024)/(0.00032))}{ln(2)}

Solve for x: 2^x*0.2^5=2^{10}

The solution is x=(ln(\frac{1024)/(0.00032))}{ln(2)}

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2^{x} \cdot 0. 2^{5} = 2^{10}

x = \frac{ln ( \frac{1024}{0.00032} )}{ln ( 2 )}

Decimal Notation

x = 21.60964 \dots

Solution steps

2^{x} \cdot 0. 2^{5} = 2^{10}

Divide both sides by

0. 2^{5}

2^{x} = \frac{2 ^{10}}{0. 2 ^{5}}

Simplify

2^{x} = \frac{1024}{0.00032}

Apply exponent rules

x ln (2) = ln (\frac{1024}{0.00032})

Solve

x ln (2) = ln (\frac{1024}{0.00032}) : x = \frac{ln ( \frac{1024}{0.00032} )}{ln ( 2 )}

x = \frac{ln ( \frac{1024}{0.00032} )}{ln ( 2 )}

2^{2 x + 1} - 2^{x + 4} = 2^{x + 2} - 32

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

4^{x} + 1 0^{x} = 2 5^{x}

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

(2^{x})^{6} = (2^{9})^{2}

What is the answer to 2^x*0.2^5=2^{10} ?
The answer to 2^x*0.2^5=2^{10} is x=(ln(\frac{1024)/(0.00032))}{ln(2)}
Solve for x: 2^x*0.2^5=2^{10}
The solution is x=(ln(\frac{1024)/(0.00032))}{ln(2)}