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Solnce55 [7]
4 years ago
12

Solve the expression p c^{t}=v b^{t} for t assuming that all other letters are positive constants

Mathematics
1 answer:
Temka [501]4 years ago
7 0

Move all the exponentials to one side, and all the constants to the other:

\dfrac{c^t}{b^t} = \dfrac{v}{p}

You can rewrite the left hand side as

\left(\dfrac{c}{b}\right)^t = \dfrac{v}{p}

Consider the logarithm base \frac{c}{b} of both sides:

log_{\frac{c}{b}}\left(\dfrac{c}{b}\right)^t = log_{\frac{c}{b}}\left(\dfrac{v}{p} \right)

Logarithm and exponential simplifies:

t = log_{\frac{c}{b}}\left(\dfrac{v}{p} \right)

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