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y-4-10-2x-Express-x-in-terms-of-y-giving-an-exact-simplified-answer-in-terms-of-log-base-10-




Question Number 193363 by MATHEMATICSAM last updated on 11/Jun/23
y = 4 × 10^(2x)   Express x in terms of y, giving an exact  simplified answer in terms of log base 10.
$${y}\:=\:\mathrm{4}\:×\:\mathrm{10}^{\mathrm{2}{x}} \\ $$$$\mathrm{Express}\:{x}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:{y},\:\mathrm{giving}\:\mathrm{an}\:\mathrm{exact} \\ $$$$\mathrm{simplified}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{log}\:\mathrm{base}\:\mathrm{10}. \\ $$
Answered by aba last updated on 11/Jun/23
y=4×10^(2x)  ⇒ 10^(2x) =(y/4) ⇒ x=(1/2)log_(10) ((y/4))
$$\mathrm{y}=\mathrm{4}×\mathrm{10}^{\mathrm{2x}} \:\Rightarrow\:\mathrm{10}^{\mathrm{2x}} =\frac{\mathrm{y}}{\mathrm{4}}\:\Rightarrow\:\mathrm{x}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{log}_{\mathrm{10}} \left(\frac{\mathrm{y}}{\mathrm{4}}\right) \\ $$

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