Solve the equation by expressing each side as a power of the same base and then equating exponents.

9^(x - 9)/8= sqrt of 9
i got 13

4^(x + 10) = 8^(x - 6)
i got 38

Solve the exponential equation. Express the solution set in terms of natural logarithms.

2^8x = 4.5
i got {ln 4.5/8 ln 2}

Solve the exponential equation. Express the solution set in terms of natural logarithms.

4^(x + 4) = 5^(2x + 5)-This question I don't understand.

9^(x - 9)/8= sqrt of 9

i got 13

Correct!
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4^(x + 10) = 8^(x - 6)
i got 38

Correct! Here's my work:

4^(x+10)=(2^2)^(x+10)
8^(x-6)=(2^3)^(x-6)
2(x+10)=3(x-6)
Distribute
2x+20=3x-18
-x=-38
x=38
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Solve the exponential equation. Express the solution set in terms of natural logarithms.

2^8x = 4.5
i got {ln 4.5/8 ln 2}

Correct! I checked the answer with my calculator for you. It's right! :-)

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Solve the exponential equation. Express the solution set in terms of natural logarithms.

4^(x + 4) = 5^(2x + 5)-This question I don't understand.

I'm not sure I do either. I'll post back if I figure it out. Sorry.

4^(x + 4) = 5^(2x + 5)

Take logs to base e of both sides
(x+4) ln4 = (2x+5)ln 5
(x+4)/(2x+5) = (ln5)/(ln4)= 1.161
Solve for x

1,2,3,4

what is x

4 - x/4 = 5

To solve the exponential equation 4^(x + 4) = 5^(2x + 5), you can take the natural logarithm of both sides. Here's how to do it step by step:

1. Take the natural logarithm (ln) of both sides of the equation:
ln(4^(x + 4)) = ln(5^(2x + 5))

2. Apply the property of logarithms that states: ln(a^b) = b * ln(a)
(x + 4) * ln(4) = (2x + 5) * ln(5)

3. Use the distributive property to simplify the equation:
x * ln(4) + 4 * ln(4) = 2x * ln(5) + 5 * ln(5)

4. Group the x terms together and the constant terms together:
x * ln(4) - 2x * ln(5) = 5 * ln(5) - 4 * ln(4)

5. Factor out the x term on the left side of the equation:
x * (ln(4) - 2 * ln(5)) = 5 * ln(5) - 4 * ln(4)

6. Divide both sides of the equation by (ln(4) - 2 * ln(5)):
x = (5 * ln(5) - 4 * ln(4)) / (ln(4) - 2 * ln(5))

The solution set for this exponential equation can be expressed in terms of natural logarithms as:
x = (5 * ln(5) - 4 * ln(4)) / (ln(4) - 2 * ln(5))

Please note that ln(4) and ln(5) represent the natural logarithms of 4 and 5 respectively.