Evaluate log0.5 16
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Let,
⇒log0.5 16=x⇒16=(0.5)x⇒16=(510)x⇒24=(12)x⇒24=(2−1)x⇒24=2−x⇒−x=4⇒x=−4.\Rightarrow \text{log}_{0.5} \space 16 = x \\[1em] \Rightarrow 16 = (0.5)^x \\[1em] \Rightarrow 16 = \Big(\dfrac{5}{10}\Big)^x \\[1em] \Rightarrow 2^4 = \Big(\dfrac{1}{2}\Big)^x \\[1em] \Rightarrow 2^4 = (2^{-1})^x \\[1em] \Rightarrow 2^4 = 2^{-x} \\[1em] \Rightarrow -x = 4 \\[1em] \Rightarrow x = -4.⇒log0.5 16=x⇒16=(0.5)x⇒16=(105)x⇒24=(21)x⇒24=(2−1)x⇒24=2−x⇒−x=4⇒x=−4.
Hence, log0.5 16 = -4.
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