What is the solution of log(t-3) = log(17-4t)?

posted on December 17, 2021

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What is the solution of log(t-3) = log(17-4t)?

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mathrm {The : solution : is} :

t = 4

Step by step explanation:

Because of the expression

log left (t-3 right) : = : log left (17-4t right)

$mathrm {Apply : log : rule: : : If} : log _b left (f left (x right) right) = log _b left (g left (x right)) right) : mathrm {then} : f left (x right) = g left (x right)$

t-3 = 17-4t

mathrm {Add :} 3 mathrm {: to : both : sides}

t-3 + 3 = 17-4t + 3

t = -4t + 20

mathrm {Add :} 4t mathrm {: to : both : sides}

t + 4t = -4t + 20 + 4t

5t = 20

mathrm {Divide : both : sides : with :} 5

$frac {5t} {5} = frac {20} {5}$

t = 4

Therefore, mathrm {the : solution : is} :

t = 4

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