1) log9x + 2log3x = 5

Rewrite the logarithms using the power rule:

log$9x$ + log$3x$^2 = 5

Combine the logarithms using the product and power rules:

log$9x$ + log$9x$^2 = 5

Simplify the expression:

log$9x$ + log$81x^2$ = 5

Combine the logarithms using the product rule:

log$9x\ast 81x^2$ = 5

Simplify the expression:

log$729x^3$ = 5

Convert to exponential form:

729x^3 = 10^5

729x^3 = 100000

x^3 = 100000 / 729

x^3 = 137.174

x = ∛137.174

x = 5.600

2) log2$x^2-3$ + 1 = log2$6x-10$

Subtract 1 from both sides:

log2$x^2-3$ = log2$6x-10$ - 1

Use the properties of logarithms to combine the logarithms on the right side:

log2$x^2-3$ = log2$(6x-10)/2$

Since the bases are the same, the arguments must be equal:

x^2 - 3 = $6x-10$ / 2

Simplify the equation:

2x^2 - 6 = 6x - 10

Rearrange the equation to set it equal to zero:

2x^2 - 6x + 4 = 0

Solve the quadratic equation by factoring or using the quadratic formula:

$x-2$$2x-2$ = 0

x = 2 or x = 1

Therefore, the solutions to the equation are x = 2 or x = 1.