How do you solve the exponential equation $10^{x - 3} = 100^{4 x - 5}$ $10^(x-3)=100^(4x-5)$ ?

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How do you solve the exponential equation $10^{x - 3} = 100^{4 x - 5}$ $10^(x-3)=100^(4x-5)$ ?

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Answer 1 · 2017-03-08T18:42:49

$x = 1$ $x=1$

Explanation:

Express the exponential on the right side with a $base of 10$ $color(blue)"base of 10"$

$\Rightarrow 10^{x - 3} = {(10^{2})}^{4 x - 5}$ $rArr10^(x-3)=(10^2)^(4x-5)$

$\Rightarrow 10^{x - 3} = 10^{8 x - 10}$ $rArr10^(x-3)=10^(8x-10)$

Since the bases on both sides are 10 then equate the exponents.

$\Rightarrow 8 x - 10 = x - 3$ $rArr8x-10=x-3$

$\Rightarrow 7 x = 7$ $rArr7x=7$

$\Rightarrow x = 1 is the solution$ $rArrx=1" is the solution"$

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How do you solve the exponential equation $10^{x - 3} = 100^{4 x - 5}$ $10^(x-3)=100^(4x-5)$ ?

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How do you solve the exponential equation $10^{x - 3} = 100^{4 x - 5}$ $10^(x-3)=100^(4x-5)$ ?