Answer:
-5/48
Step-by-step explanation:
(8 · 2⁷ˣ)⁴ = (1/16)⁵ˣ · 128
<em>Take log of both sides.</em>
log (8 · 2⁷ˣ)⁴ = log ((1/16)⁵ˣ · 128)
<em>Use log exponent/product rules.</em>
4 log (8 · 2⁷ˣ) = log (1/16)⁵ˣ + log 128
<em>Use log exponent/product rules.</em>
4 (log 8 + log (2⁷ˣ)) = 5x log (1/16) + log 128
<em>Use log exponent rule.</em>
4 (log 8 + 7x log 2) = 5x log (1/16) + log 128
<em>Distribute.</em>
4 log 8 + 28x log 2 = 5x log (1/16) + log 128
<em>Write as powers of 2.</em>
4 log 2³ + 28x log 2 = 5x log (2⁻⁴) + log 2⁷
<em>Use log exponent rule.</em>
12 log 2 + 28x log 2 = -20x log 2 + 7 log 2
<em>Combine like terms.</em>
5 log 2 + 48x log 2 = 0
<em>Divide by log 2.</em>
5 + 48x = 0
<em>Solve for x.</em>
x = -5/48
