How do you solve this equation? #aln(ax)=ln(tb)#
#aln(ax)=ln(tb)#
Solve for x.
Solve for x.
#x = a  root(a)(1/(tb))" "# if#a != 0#
#x < 0" "# if#a = 0#
Your equation looks like this
You're dealing with natural logs, so right from the start you know that you must have
In this case we have
So
Hence
Then taking exponents of both sides
So our equation simplifies to
Hence
is a welldefined positive Real number.
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To solve the equation aln(ax) = ln(tb), follow these steps:

Use the property of logarithms to rewrite the equation: ln((t  b)^{a}) = ln(e^{aln(ax)})

Apply the property of logarithms: ln(a^b) = b * ln(a): a * ln(t  b) = aln(e^{ln(ax)})

Since ln(e^x) = x, the equation simplifies to: a * ln(t  b) = a * ln(a  x)

Divide both sides by a: ln(t  b) = ln(a  x)

Since the natural logarithm function ln(x) is onetoone, its inverse is the exponential function e^x. Therefore, if ln(t  b) = ln(a  x), then t  b = a  x.

Solve for x: x = a  (t  b) x = a  t + b

Rearrange the terms: x = b  t + a
So, the solution to the equation is x = b  t + a.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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