What is the answer to (1/2)^{a+1}+(1/2)^{a+3}+(1/2)^{a+5}=42 ?

The answer to (1/2)^{a+1}+(1/2)^{a+3}+(1/2)^{a+5}=42 is a=-6

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(1/2)^{a+1}+(1/2)^{a+3}+(1/2)^{a+5}=42

(\frac{1}{2})^{a + 1} + (\frac{1}{2})^{a + 3} + (\frac{1}{2})^{a + 5} = 42

a = - 6

Solution steps

(\frac{1}{2})^{a + 1} + (\frac{1}{2})^{a + 3} + (\frac{1}{2})^{a + 5} = 42

Factor

(\frac{1}{2})^{a + 1} + (\frac{1}{2})^{a + 3} + (\frac{1}{2})^{a + 5} : \frac{21}{16} (\frac{1}{2})^{a + 1}

\frac{21}{16} (\frac{1}{2})^{a + 1} = 42

Multiply both sides by

16

21 (\frac{1}{2})^{a + 1} = 672

Divide both sides by

21

(\frac{1}{2})^{a + 1} = 32

Apply exponent rules

- (a + 1) = 5

Solve

- (a + 1) = 5 : a = - 6

a = - 6

2^{x} \cdot 2^{1} - 6 = - 23 \cdot 2^{x} \cdot 2^{1}

19 2^{x} = 3.967

1 3^{x} = 30

29.5 = 1 0^{(\frac{x}{10})}

4^{\frac{1}{x - 2}} = \frac{( lo g _{10} ( 10 ) )}{2}

What is the answer to (1/2)^{a+1}+(1/2)^{a+3}+(1/2)^{a+5}=42 ?
The answer to (1/2)^{a+1}+(1/2)^{a+3}+(1/2)^{a+5}=42 is a=-6
Solve for a: (1/2)^{a+1}+(1/2)^{a+3}+(1/2)^{a+5}=42
The solution is a=-6