What is the answer to 3420=3270(0.97)^{2x-5}+920 ?

The answer to 3420=3270(0.97)^{2x-5}+920 is x=-16.41539…ln((214.68350…)/(327))

Solve for x: 3420=3270(0.97)^{2x-5}+920

The solution is x=-16.41539…ln((214.68350…)/(327))

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3420 = 3270 (0.97)^{2 x - 5} + 920

x = - 16.41539 \dots ln (\frac{214.68350 \dots}{327})

Decimal Notation

x = 6.90752 \dots

Solution steps

3420 = 3270 (0.97)^{2 x - 5} + 920

Switch sides

3270 \cdot 0.9 7^{2 x - 5} + 920 = 3420

Move

920

to the right side

3270 \cdot 0.9 7^{2 x - 5} = 2500

Divide both sides by

3270

0.9 7^{2 x - 5} = \frac{250}{327}

Apply exponent rules

(2 x - 5) ln (0.97) = ln (\frac{250}{327})

Solve

(2 x - 5) ln (0.97) = ln (\frac{250}{327}) : x = - 16.41539 \dots ln (\frac{214.68350 \dots}{327})

x = - 16.41539 \dots ln (\frac{214.68350 \dots}{327})

2 (3)^{2 x + 1} = 3 - 7 (3^{x})

4^{x} = \frac{1}{128}

3^{2 x - 2} = \frac{1}{243}

250 = \frac{( e ^{42 r} - 1 )}{r}

(5^{2})^{x} = 125

What is the answer to 3420=3270(0.97)^{2x-5}+920 ?
The answer to 3420=3270(0.97)^{2x-5}+920 is x=-16.41539…ln((214.68350…)/(327))
Solve for x: 3420=3270(0.97)^{2x-5}+920
The solution is x=-16.41539…ln((214.68350…)/(327))