Questions: Solve 1/128 = 2^(5x+3) x=

Solution Steps

To solve the equation \(\frac{1}{128} = 2^{5x+3}\), we first express \(\frac{1}{128}\) as a power of 2. Since \(128 = 2^7\), we have \(\frac{1}{128} = 2^{-7}\). This gives us the equation \(2^{-7} = 2^{5x+3}\). By equating the exponents, we solve for \(x\).

We start with the equation

\[ \frac{1}{128} = 2^{5x + 3} \]

We can express \(\frac{1}{128}\) as a power of 2:

\[ \frac{1}{128} = 2^{-7} \]

Thus, we rewrite the equation as:

\[ 2^{-7} = 2^{5x + 3} \]

Since the bases are the same, we can equate the exponents:

\[ -7 = 5x + 3 \]

To isolate \(x\), we first subtract 3 from both sides:

\[ -7 - 3 = 5x \]

This simplifies to:

\[ -10 = 5x \]

Now, divide both sides by 5:

\[ x = -2 \]

Final Answer