solve the exponential equation. 130^7x+3=170 (1 point)
Responses
0.3375
-0.2932
-0.2418
-0.2778
To solve the exponential equation 130^(7x + 3) = 170, we need to isolate the exponent.
Take the natural logarithm (ln) of both sides to remove the base 130:
ln(130^(7x + 3)) = ln(170)
Using the logarithmic property ln(a^b) = b * ln(a), we can simplify the equation to:
(7x + 3) * ln(130) = ln(170)
Divide both sides by the natural logarithm of 130:
7x + 3 = ln(170) / ln(130)
Subtract 3 from both sides:
7x = ln(170) / ln(130) - 3
Next, divide both sides by 7:
x = (ln(170) / ln(130) - 3) / 7
Using a calculator, we can approximate the value:
x ≈ -0.2778
Therefore, the solution to the equation 130^(7x + 3) = 170 is approximately -0.2778.