Exponetial Functions

In the following exponential relations, solve for x using logarithms. Round your answers to 4 decimal places.

a)
5^3x=65

b)
2^2x+3=80

Joseph/Matt/Mark/Chris -- please use the same name for your posts.

Okay,but can i get assistance?

To solve the exponential equations using logarithms, follow these steps:

Step 1: Take the logarithm of both sides of the equation. The choice of logarithm base is not important, but usually, logarithms with bases 10 (log) or e (ln) are used. In these examples, we will use the natural logarithm (ln).

Step 2: Apply logarithmic properties to simplify the equation.

Step 3: Solve for x by isolating it.

Now let's solve each of the given equations using logarithms:

a) 5^(3x) = 65

Step 1: Take the natural logarithm of both sides:
ln[5^(3x)] = ln(65)

Step 2: Apply the exponent rule for logarithms:
3x * ln(5) = ln(65)

Step 3: Solve for x by isolating it:
3x = ln(65) / ln(5)
x = (ln(65) / ln(5)) / 3

Calculate the right side using a calculator, then divide by 3 to get the approximate value of x.

b) 2^(2x+3) = 80

Step 1: Take the natural logarithm of both sides:
ln[2^(2x+3)] = ln(80)

Step 2: Apply the exponent rule for logarithms:
(2x+3) * ln(2) = ln(80)

Step 3: Solve for x by isolating it:
2x+3 = ln(80) / ln(2)
x = (ln(80) / ln(2)) - (3/2)

Calculate the right side using a calculator, then subtract 3/2 to get the approximate value of x, rounded to 4 decimal places.