Question

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

Answer 1

Answer:

t=4

Step-by-step explanation:

The given logarithmic equation is:

$\ log(t - 3) = \ log(17 - 4t)$

We want to solve for,

We take antilogarithm to get:

$t - 3 = 17 - 4t$

Combine similar terms to get:

$t + 4t = 17 + 3$

Simplify to obtain:

$5t = 20$

Divide both sides by 5

$t = \frac{20}{5} = 4$

Answer 2

Answer:

$\mathrm{The\:solution\:is}$:

$t=4$

Step-by-step explanation:

Given the expression

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

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

$t-3=17-4t$

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

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

$t=-4t+20$

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

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

$5t=20$

$\mathrm{Divide\:both\:sides\:by\:}5$

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

$t=4$

Therefore, $\mathrm{the\:solution\:is}$:

$t=4$