What is the solution for 3.5^(3x + 1) = 65.4?

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the equation ( 3.5)^(3x+1) = 65.4

We need to find the values of x that satisfies the equation.

We will apply the logarithm to both sides.

==> log 3.5^(3x+1) = log 65.4

==> (3x+1)*log 3.5 = log 65.4

==> 3x+1 = log 65.4/ log 3.5

==> 3x +1 = 1.8156/ 0.5411

==> 3x + 1 = 3.337

==> 3x = 3.337 -1 = 2.337

==> x = 2.337/3 = 0.7790

Then the solution is x = 0.7790

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to find the solution for the equation 3.5^(3x + 1) = 65.4

An easy way to determine the value for x is to use logarithms. Take the log of both the sides

log 3.5^(3x + 1) = log 65.4

use the the property of logarithms that log a^b = b*log a

=> (3x + 1)* log 3.5 = log 65.4

=> 3x + 1 = log 65.4 / log 3.5

=> 3x = (log 65.4 / log 3.5) - 1

=> x = [(log 65.4 / log 3.5)]/3 - 1/3

=> x = 0.7790 approximately

The required value of x = [(log 65.4 / log 3.5)]/3 - 1/3

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