Question

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

Answer 1

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

`t=4`

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`

`(5t)/(5)=(20)/(5)`

`t=4`

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

`t=4`

Answer 2

t=4

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 = (20)/(5) = 4`