Solve the exponential equation, round to the nearest hundredth.

Question

3^4x+5=130

Answer 1

Take the common logarithm of both sides:

 

log 3^{4x + 5} = log 130

 

Applying the power rule for logarithms, this becomes

 

(4x+5) log 3 = log 130

 

Now, using ordinary algebra:

 

[(4x+5) log 3] / (log 3 )= (log 130) / (log 3)

 

4x+5 = (log 130) / (log 3)

4x+5 - 5 = [(log 130) / (log 3) ] - 5

 

4x  = [(log 130) / (log 3) ] - 5

 

4x / 4 = {[(log 130) / (log 3) ] - 5} / 4

 

x= {[(log 130) / (log 3) ] - 5} / 4

 

Approximating to four digits:

 

x = (2.1139 / 0.4771 - 5) / 4 = −0.1423

Answer 2

3^(4X+5)=130

log(3^[4x+5])=log130

(4x+5)log3=log130

4x+5=log130/log3

4x+5=2.11394335/0.47712125

4x+5=4.43062

4x=-5+4.43062

4x=-0.569379

x=-0.569379/4

x=-0.14234479

x=-0.14