Solve for exponential equation. 7*5^{3x-1}+3=15

inurbandojoa

inurbandojoa

Answered question

2022-11-13

Solve the exponential equation.
7 5 3 x 1 + 3 = 15

Answer & Explanation

Kayleigh Cross

Kayleigh Cross

Beginner2022-11-14Added 19 answers

7 5 3 x 1 + 3 = 15
Subtracting 3 on both sides,
7 5 3 x 1 + 3 3 = 15 3 7 5 3 x 1 = 12
Dividing both sides by 7,
5 3 x 1 = 12 7
Taking natural logarithm on both sides,
ln   5 3 x 1 = ln   ( 12 7 )
We have power rule: ln ab = b ln a. Using this,
( 3 x 1 )   ln   5 = ln   ( 12 7 )
Dividing both sides by (ln 5), we get
( 3 x 1 )   = ln   ( 12 7 ) ln   5
Adding 1 on both sides, we get
3 x = 1 + ln   ( 12 7 ) ln   5
Dividing both sides by 3, we get
x = 1 3 ( 1 + ln   ( 12 7 ) ln   5 )

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