Question

Hello, I do not anderstand this at all. I have been working on radicals and stuff, but this goes way above my head. Please help.

Answer 1

Answer:

x = $\frac{5}{7}$

Step-by-step explanation:

We can start simplifying this equation by expanding the parenthesis and cross multiplying.

$(7^x)^4 = \frac{7^2 * 7^3}{7^{3x}} = \\\\\\7^{4x} = \frac{7^5}{7^{3x}}\\\\\\7^5 = 7^{7x}$

The exponent 5 and 7x are equal:

$\longmapsto$Divide both sides by 7

$5 = 7x\\\\x = \frac57$

-Chetan K

Answer 2

Answer:

• 5/7

Step-by-step explanation:

Use identities:

• $(a^b)^c = a^{bc}\\a^ba^c=a^{b+c}\\a^b/a^c=a^{b-c}\\a^b=a^c -->b = c$

Solve as below:

• (7ˣ)⁴ = 7² · 7³ / 7³ˣ
• 7⁴ˣ = 7⁵ / 7³ˣ
• 7⁴ˣ = 7⁵ ⁻ ³ˣ
• 4x = 5 - 3x
• 4x + 3x = 5
• 7x = 5
• x = 5/7