# What is the value of #x# where the tangent to #y -1 = 3^x# has a slope of #5#?

Start by finding the derivative of the function.

Differentiate the left hand side using the chain rule and the right hand side using the product rule.

Hopefully this helps!

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To find the value of x where the tangent to y - 1 = 3^x has a slope of 5, we need to differentiate the equation with respect to x. The derivative of y - 1 = 3^x is dy/dx = 3^x * ln(3).

To find the slope of the tangent line, we set dy/dx equal to 5 and solve for x:

5 = 3^x * ln(3)

Divide both sides by ln(3):

5/ln(3) = 3^x

Take the logarithm of both sides with base 3:

log3(5/ln(3)) = x

Therefore, the value of x where the tangent to y - 1 = 3^x has a slope of 5 is x = log3(5/ln(3)).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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